| ID | problem | ODE | Solved? | Maple | Mma | Sympy |
| 1.1.1 |
\begin{align*}
y^{\prime }&=f \left (x \right ) \\
\end{align*} |
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| 1.1.2 |
\begin{align*}
y^{\prime }&=f \left (y\right ) \\
\end{align*} |
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| 1.1.3 |
\begin{align*}
y^{\prime }&=f \left (x \right ) g \left (y\right ) \\
\end{align*} |
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| 1.1.4 |
\begin{align*}
g \left (x \right ) y^{\prime }&=f_{1} \left (x \right ) y+f_{0} \left (x \right ) \\
\end{align*} |
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| 1.1.5 |
\begin{align*}
g \left (x \right ) y^{\prime }&=f_{1} \left (x \right ) y+f_{n} \left (x \right ) y^{n} \\
\end{align*} |
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| 1.1.6 |
\begin{align*}
y^{\prime }&=f \left (\frac {y}{x}\right ) \\
\end{align*} |
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| ID | problem | ODE | Solved? | Maple | Mma | Sympy |
| 1 |
\begin{align*}
y^{\prime }&=a y^{2}+b x +c \\
\end{align*} |
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| 2 |
\begin{align*}
y^{\prime }&=y^{2}-a^{2} x^{2}+3 a \\
\end{align*} |
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| 3 |
\begin{align*}
y^{\prime }&=y^{2}+a^{2} x^{2}+b x +c \\
\end{align*} |
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| 4 |
\begin{align*}
y^{\prime }&=a y^{2}+b \,x^{n} \\
\end{align*} |
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| 5 |
\begin{align*}
y^{\prime }&=y^{2}+x^{n -1} a n -a^{2} x^{2 n} \\
\end{align*} |
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| 6 |
\begin{align*}
y^{\prime }&=a y^{2}+b \,x^{2 n}+c \,x^{n -1} \\
\end{align*} |
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| 7 |
\begin{align*}
y^{\prime }&=a \,x^{n} y^{2}+b \,x^{-n -2} \\
\end{align*} |
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| 8 |
\begin{align*}
y^{\prime }&=a \,x^{n} y^{2}+b \,x^{m} \\
\end{align*} |
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| 10 |
\begin{align*}
y^{\prime }&=a \,x^{n} y^{2}+b m \,x^{m -1}-a \,b^{2} x^{n +2 m} \\
\end{align*} |
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| 11 |
\begin{align*}
y^{\prime }&=\left (a \,x^{2 n}+b \,x^{n -1}\right ) y^{2}+c \\
\end{align*} |
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| 12 |
\begin{align*}
\left (a_{2} x +b_{2} \right ) \left (y^{\prime }+\lambda y^{2}\right )+a_{0} x +b_{0}&=0 \\
\end{align*} |
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| 13 |
\begin{align*}
x^{2} y^{\prime }&=a \,x^{2} y^{2}+b \\
\end{align*} |
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| 14 |
\begin{align*}
x^{2} y^{\prime }&=y^{2} x^{2}-a^{2} x^{4}+a \left (1-2 b \right ) x^{2}-b \left (b +1\right ) \\
\end{align*} |
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| 15 |
\begin{align*}
x^{2} y^{\prime }&=a \,x^{2} y^{2}+b \,x^{n}+c \\
\end{align*} |
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| 17 |
\begin{align*}
\left (c_{2} x^{2}+b_{2} x +a_{2} \right ) \left (y^{\prime }+\lambda y^{2}\right )+a_{0}&=0 \\
\end{align*} |
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| 18 |
\begin{align*}
x^{4} y^{\prime }&=-y^{2} x^{4}-a^{2} \\
\end{align*} |
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| 19 |
\begin{align*}
a \,x^{2} \left (x -1\right )^{2} \left (y^{\prime }+\lambda y^{2}\right )+b \,x^{2}+c x +s&=0 \\
\end{align*} |
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| 20 |
\begin{align*}
\left (a \,x^{2}+b x +c \right )^{2} \left (y^{\prime }+y^{2}\right )+A&=0 \\
\end{align*} |
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| 21 |
\begin{align*}
x^{n +1} y^{\prime }&=x^{2 n} a y^{2}+c \,x^{m}+d \\
\end{align*} |
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| 22 |
\begin{align*}
\left (a \,x^{n}+b \right ) y^{\prime }&=b y^{2}+a \,x^{-2+n} \\
\end{align*} |
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| 23 |
\begin{align*}
\left (a \,x^{n}+b \,x^{m}+c \right ) \left (y^{\prime }-y^{2}\right )+a n \left (n -1\right ) x^{-2+n}+b m \left (m -1\right ) x^{m -2}&=0 \\
\end{align*} |
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| 24 |
\begin{align*}
y^{\prime }&=a y^{2}+b y+c x +k \\
\end{align*} |
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| 25 |
\begin{align*}
y^{\prime }&=y^{2}+a \,x^{n} y+a \,x^{n -1} \\
\end{align*} |
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| 26 |
\begin{align*}
y^{\prime }&=y^{2}+a \,x^{n} y+b \,x^{n -1} \\
\end{align*} |
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| 27 |
\begin{align*}
y^{\prime }&=y^{2}+\left (x \alpha +\beta \right ) y+a \,x^{2}+b x +c \\
\end{align*} |
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| 28 |
\begin{align*}
y^{\prime }&=y^{2}+a \,x^{n} y-a b \,x^{n}-b^{2} \\
\end{align*} |
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| 30 |
\begin{align*}
y^{\prime }&=a \,x^{n} y^{2}+b \,x^{m} y+x^{m} b c -a \,c^{2} x^{n} \\
\end{align*} |
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| 31 |
\begin{align*}
y^{\prime }&=a \,x^{n} y^{2}-a \,x^{n} \left (b \,x^{m}+c \right ) y+b m \,x^{m -1} \\
\end{align*} |
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| 32 |
\begin{align*}
y^{\prime }&=-a n \,x^{n -1} y^{2}+c \,x^{m} \left (a \,x^{n}+b \right ) y-c \,x^{m} \\
\end{align*} |
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| 33 |
\begin{align*}
y^{\prime }&=a \,x^{n} y^{2}+b \,x^{m} y+c k \,x^{-1+k}-b c \,x^{m +k}-a \,c^{2} x^{n +2 k} \\
\end{align*} |
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| 34 |
\begin{align*}
y^{\prime } x&=a y^{2}+b y+c \,x^{2 b} \\
\end{align*} |
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| 35 |
\begin{align*}
y^{\prime } x&=a y^{2}+b y+c \,x^{n} \\
\end{align*} |
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| 36 |
\begin{align*}
y^{\prime } x&=a y^{2}+\left (n +b \,x^{n}\right ) y+c \,x^{2 n} \\
\end{align*} |
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| 37 |
\begin{align*}
y^{\prime } x&=x y^{2}+a y+b \,x^{n} \\
\end{align*} |
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| 38 |
\begin{align*}
y^{\prime } x +a_{3} x y^{2}+a_{2} y+a_{1} x +a_{0}&=0 \\
\end{align*} |
✓ |
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| 39 |
\begin{align*}
y^{\prime } x&=a \,x^{n} y^{2}+b y+c \,x^{-n} \\
\end{align*} |
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| 40 |
\begin{align*}
y^{\prime } x&=a \,x^{n} y^{2}+m y-a \,b^{2} x^{n +2 m} \\
\end{align*} |
✓ |
✓ |
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| 41 |
\begin{align*}
y^{\prime } x&=x^{2 n} y^{2}+\left (m -n \right ) y+x^{2 m} \\
\end{align*} |
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| 42 |
\begin{align*}
y^{\prime } x&=a \,x^{n} y^{2}+b y+c \,x^{m} \\
\end{align*} |
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| 43 |
\begin{align*}
y^{\prime } x&=x^{2 n} a y^{2}+\left (b \,x^{n}-n \right ) y+c \\
\end{align*} |
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| 44 |
\begin{align*}
y^{\prime } x&=a \,x^{2 n +m} y^{2}+\left (b \,x^{n +m}-n \right ) y+c \,x^{m} \\
\end{align*} |
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| 45 |
\begin{align*}
\left (a_{2} x +b_{2} \right ) \left (y^{\prime }+\lambda y^{2}\right )+\left (a_{1} x +b_{1} \right ) y+a_{0} x +b_{0}&=0 \\
\end{align*} |
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| 46 |
\begin{align*}
\left (a x +c \right ) y^{\prime }&=\alpha \left (a y+b x \right )^{2}+\beta \left (a y+b x \right )-b x +\gamma \\
\end{align*} |
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| 47 |
\begin{align*}
2 x^{2} y^{\prime }&=2 y^{2}+y x -2 a^{2} x \\
\end{align*} |
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| 48 |
\begin{align*}
2 x^{2} y^{\prime }&=2 y^{2}+3 y x -2 a^{2} x \\
\end{align*} |
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| 49 |
\begin{align*}
x^{2} y^{\prime }&=a \,x^{2} y^{2}+b x y+c \\
\end{align*} |
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| 50 |
\begin{align*}
x^{2} y^{\prime }&=c \,x^{2} y^{2}+\left (a \,x^{2}+b x \right ) y+\alpha \,x^{2}+\beta x +\gamma \\
\end{align*} |
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| 51 |
\begin{align*}
x^{2} y^{\prime }&=a \,x^{2} y^{2}+b x y+c \,x^{n}+s \\
\end{align*} |
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| 52 |
\begin{align*}
x^{2} y^{\prime }&=a \,x^{2} y^{2}+b x y+c \,x^{2 n}+s \,x^{n} \\
\end{align*} |
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| 53 |
\begin{align*}
x^{2} y^{\prime }&=c \,x^{2} y^{2}+\left (a \,x^{n}+b \right ) x y+\alpha \,x^{2 n}+\beta \,x^{n}+\gamma \\
\end{align*} |
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✓ |
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| 54 |
\begin{align*}
x^{2} y^{\prime }&=\left (\alpha \,x^{2 n}+\beta \,x^{n}+\gamma \right ) y^{2}+\left (a \,x^{n}+b \right ) x y+c \,x^{2} \\
\end{align*} |
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| 55 |
\begin{align*}
\left (x^{2}-1\right ) y^{\prime }+\lambda \left (1-2 y x +y^{2}\right )&=0 \\
\end{align*} |
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✓ |
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| 56 |
\begin{align*}
\left (a \,x^{2}+b \right ) y^{\prime }+\alpha y^{2}+\beta x y+\frac {b \left (a +\beta \right )}{\alpha }&=0 \\
\end{align*} |
✓ |
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| 57 |
\begin{align*}
\left (a \,x^{2}+b \right ) y^{\prime }+\alpha y^{2}+\beta x y+\gamma &=0 \\
\end{align*} |
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✓ |
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| 58 |
\begin{align*}
\left (a \,x^{2}+b \right ) y^{\prime }+y^{2}-2 y x +\left (1-a \right ) x^{2}-b&=0 \\
\end{align*} |
✓ |
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| 59 |
\begin{align*}
\left (a \,x^{2}+b x +c \right ) y^{\prime }&=y^{2}+\left (2 \lambda x +b \right ) y+\lambda \left (\lambda -a \right ) x^{2}+\mu \\
\end{align*} |
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| 60 |
\begin{align*}
\left (a \,x^{2}+b x +c \right ) y^{\prime }&=y^{2}+\left (a x +\mu \right ) y-\lambda ^{2} x^{2}+\lambda \left (b -\mu \right ) x +\lambda c \\
\end{align*} |
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| 61 |
\begin{align*}
\left (a_{2} x^{2}+b_{2} x +c_{2} \right ) y^{\prime }&=y^{2}+\left (a_{1} x +b_{1} \right ) y-\lambda \left (\lambda +a_{1} -a_{2} \right ) x^{2}+\lambda \left (b_{2} -b_{1} \right ) x +\lambda c_{2} \\
\end{align*} |
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| 62 |
\begin{align*}
\left (a_{2} x^{2}+b_{2} x +c_{2} \right ) y^{\prime }&=y^{2}+\left (a_{1} x +b_{1} \right ) y+a_{0} x^{2}+b_{0} x +c_{0} \\
\end{align*} |
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| 63 |
\begin{align*}
\left (x -a \right ) \left (x -b \right ) y^{\prime }+k \left (x +y-a \right ) \left (x +y-b \right )+y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
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| 64 |
\begin{align*}
\left (c_{2} x^{2}+b_{2} x +a_{2} \right ) \left (y^{\prime }+\lambda y^{2}\right )+\left (b_{1} x +a_{1} \right ) y+a_{0}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
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| 65 |
\begin{align*}
x^{3} y^{\prime }&=a \,x^{3} y^{2}+\left (b \,x^{2}+c \right ) y+s x \\
\end{align*} |
✓ |
✓ |
✓ |
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| 66 |
\begin{align*}
x^{3} y^{\prime }&=a \,x^{3} y^{2}+x \left (b x +c \right ) y+x \alpha +\beta \\
\end{align*} |
✗ |
✓ |
✓ |
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| 67 |
\begin{align*}
x \left (x^{2}+a \right ) \left (y^{\prime }+\lambda y^{2}\right )+\left (b \,x^{2}+c \right ) y+s x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
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| 68 |
\begin{align*}
x^{2} \left (a +x \right ) \left (y^{\prime }+\lambda y^{2}\right )+x \left (b x +c \right ) y+x \alpha +\beta &=0 \\
\end{align*} |
✓ |
✓ |
✓ |
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| 69 |
\begin{align*}
\left (a \,x^{2}+b x +e \right ) \left (-y+y^{\prime } x \right )-y^{2}+x^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
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| 70 |
\begin{align*}
x^{2} \left (x^{2}+a \right ) \left (y^{\prime }+\lambda y^{2}\right )+x \left (b \,x^{2}+c \right ) y+s&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
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| 72 |
\begin{align*}
x^{n +1} y^{\prime }&=x^{2 n} a y^{2}+b \,x^{n} y+c \,x^{m}+d \\
\end{align*} |
✓ |
✓ |
✓ |
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| 73 |
\begin{align*}
x \left (a \,x^{k}+b \right ) y^{\prime }&=\alpha \,x^{n} y^{2}+\left (\beta -a n \,x^{k}\right ) y+\gamma \,x^{-n} \\
\end{align*} |
✓ |
✓ |
✓ |
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| 74 |
\begin{align*}
x^{2} \left (a \,x^{n}-1\right ) \left (y^{\prime }+\lambda y^{2}\right )+\left (p \,x^{n}+q \right ) x y+r \,x^{n}+s&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
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| 75 |
\begin{align*}
\left (a \,x^{n}+b \,x^{m}+c \right ) y^{\prime }&=c y^{2}-b \,x^{m -1} y+a \,x^{-2+n} \\
\end{align*} |
✓ |
✗ |
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| 76 |
\begin{align*}
\left (a \,x^{n}+b \,x^{m}+c \right ) y^{\prime }&=a \,x^{-2+n} y^{2}+b \,x^{m -1} y+c \\
\end{align*} |
✓ |
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| 77 |
\begin{align*}
\left (a \,x^{n}+b \,x^{m}+c \right ) y^{\prime }&=\alpha \,x^{k} y^{2}+\beta \,x^{s} y-\alpha \,\lambda ^{2} x^{k}+\beta \lambda \,x^{s} \\
\end{align*} |
✓ |
✓ |
✓ |
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| 78 |
\begin{align*}
\left (a \,x^{n}+b \,x^{m}+c \right ) \left (-y+y^{\prime } x \right )+s \,x^{k} \left (y^{2}-\lambda \,x^{2}\right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
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| ID | problem | ODE | Solved? | Maple | Mma | Sympy |
| 1 |
\begin{align*}
y^{\prime }&=a y^{2}+b \,{\mathrm e}^{\lambda x} \\
\end{align*} |
✓ |
✓ |
✓ |
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| 2 |
\begin{align*}
y^{\prime }&=y^{2}+a \lambda \,{\mathrm e}^{\lambda x}-a^{2} {\mathrm e}^{2 \lambda x} \\
\end{align*} |
✓ |
✓ |
✓ |
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| 3 |
\begin{align*}
y^{\prime }&=\sigma y^{2}+a +b \,{\mathrm e}^{\lambda x}+c \,{\mathrm e}^{2 \lambda x} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
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| 4 |
\begin{align*}
y^{\prime }&=\sigma y^{2}+a y+b \,{\mathrm e}^{x}+c \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
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| 5 |
\begin{align*}
y^{\prime }&=y^{2}+b y+a \left (\lambda -b \right ) {\mathrm e}^{\lambda x}-a^{2} {\mathrm e}^{2 \lambda x} \\
\end{align*} |
✓ |
✓ |
✓ |
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| 6 |
\begin{align*}
y^{\prime }&=y^{2}+a \,{\mathrm e}^{\lambda x} y-a b \,{\mathrm e}^{\lambda x}-b^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
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| 7 |
\begin{align*}
y^{\prime }&=y^{2}+a \,{\mathrm e}^{2 \lambda x} \left ({\mathrm e}^{\lambda x}+b \right )^{n}-\frac {\lambda ^{2}}{4} \\
\end{align*} |
✗ |
✓ |
✗ |
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| 8 |
\begin{align*}
y^{\prime }&=y^{2}+a \,{\mathrm e}^{8 \lambda x}+b \,{\mathrm e}^{6 \lambda x}+c \,{\mathrm e}^{4 \lambda x}-\lambda ^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
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| 9 |
\begin{align*}
y^{\prime }&=a \,{\mathrm e}^{x k} y^{2}+b \,{\mathrm e}^{s x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
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| 10 |
\begin{align*}
y^{\prime }&=b \,{\mathrm e}^{\mu x} y^{2}+a \lambda \,{\mathrm e}^{\lambda x}-a^{2} b \,{\mathrm e}^{\left (2 \lambda +\mu \right ) x} \\
\end{align*} |
✓ |
✗ |
✓ |
✗ |
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| 11 |
\begin{align*}
y^{\prime }&=a \,{\mathrm e}^{\lambda x} y^{2}+b y+c \,{\mathrm e}^{-\lambda x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
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| 12 |
\begin{align*}
y^{\prime }&=a \,{\mathrm e}^{\mu x} y^{2}+\lambda y-a \,b^{2} {\mathrm e}^{\left (2 \lambda +\mu \right ) x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
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| 13 |
\begin{align*}
y^{\prime }&={\mathrm e}^{\lambda x} y^{2}+a \,{\mathrm e}^{\mu x} y+a \lambda \,{\mathrm e}^{\left (\mu -\lambda \right ) x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
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| 14 |
\begin{align*}
y^{\prime }&=-\lambda \,{\mathrm e}^{\lambda x} y^{2}+a \,{\mathrm e}^{\mu x} y-a \,{\mathrm e}^{\left (\mu -\lambda \right ) x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 15 |
\begin{align*}
y^{\prime }&=a \,{\mathrm e}^{\mu x} y^{2}+a b \,{\mathrm e}^{\left (\lambda +\mu \right ) x} y-b \lambda \,{\mathrm e}^{\lambda x} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
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| 16 |
\begin{align*}
y^{\prime }&=a \,{\mathrm e}^{x k} y^{2}+b y+c \,{\mathrm e}^{s x}+d \,{\mathrm e}^{-x k} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 17 |
\begin{align*}
y^{\prime }&=a \,{\mathrm e}^{\left (2 \lambda +\mu \right ) x} y^{2}+\left (b \,{\mathrm e}^{\left (\lambda +\mu \right ) x}-\lambda \right ) y+c \,{\mathrm e}^{\mu x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 19 |
\begin{align*}
y^{\prime }&={\mathrm e}^{\mu x} \left (y-b \,{\mathrm e}^{\lambda x}\right )^{2}+b \lambda \,{\mathrm e}^{\lambda x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 20 |
\begin{align*}
\left (a \,{\mathrm e}^{\lambda x}+b \,{\mathrm e}^{\mu x}+c \right ) y^{\prime }&=y^{2}+k \,{\mathrm e}^{\nu x} y-m^{2}+k m \,{\mathrm e}^{\nu x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 21 |
\begin{align*}
\left (a \,{\mathrm e}^{\lambda x}+b \,{\mathrm e}^{\mu x}+c \right ) \left (y^{\prime }-y^{2}\right )+a \,\lambda ^{2} {\mathrm e}^{\lambda x}+b \,\mu ^{2} {\mathrm e}^{\mu x}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| ID | problem | ODE | Solved? | Maple | Mma | Sympy |
| 22 |
\begin{align*}
y^{\prime }&=y^{2}+a x \,{\mathrm e}^{\lambda x} y+a \,{\mathrm e}^{\lambda x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 23 |
\begin{align*}
y^{\prime }&=a \,{\mathrm e}^{\lambda x} y^{2}+b \,{\mathrm e}^{-\lambda x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 24 |
\begin{align*}
y^{\prime }&=a \,{\mathrm e}^{\lambda x} y^{2}+b n \,x^{n -1}-a \,b^{2} {\mathrm e}^{\lambda x} x^{2 n} \\
\end{align*} |
✓ |
✗ |
✗ |
✗ |
|
| 25 |
\begin{align*}
y^{\prime }&={\mathrm e}^{\lambda x} y^{2}+a \,x^{n} y+a \lambda \,x^{n} {\mathrm e}^{-\lambda x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 26 |
\begin{align*}
y^{\prime }&=-\lambda \,{\mathrm e}^{\lambda x} y^{2}+a \,x^{n} {\mathrm e}^{\lambda x} y-a \,x^{n} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 27 |
\begin{align*}
y^{\prime }&=a \,{\mathrm e}^{\lambda x} y^{2}-a b \,x^{n} {\mathrm e}^{\lambda x} y+b n \,x^{n -1} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 28 |
\begin{align*}
y^{\prime }&=a \,x^{n} y^{2}+b \lambda \,{\mathrm e}^{\lambda x}-a \,b^{2} x^{n} {\mathrm e}^{2 \lambda x} \\
\end{align*} |
✓ |
✗ |
✗ |
✗ |
|
| 29 |
\begin{align*}
y^{\prime }&=a \,x^{n} y^{2}+\lambda y-a \,b^{2} x^{n} {\mathrm e}^{2 \lambda x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 30 |
\begin{align*}
y^{\prime }&=a \,x^{n} y^{2}-a b \,x^{n} {\mathrm e}^{\lambda x} y+b \lambda \,{\mathrm e}^{\lambda x} \\
\end{align*} |
✗ |
✗ |
✓ |
✗ |
|
| 31 |
\begin{align*}
y^{\prime }&=-\left (1+k \right ) x^{k} y^{2}+a \,x^{1+k} {\mathrm e}^{\lambda x} y-a \,{\mathrm e}^{\lambda x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 32 |
\begin{align*}
y^{\prime }&=a \,x^{n} y^{2}-a \,x^{n} \left (b \,{\mathrm e}^{\lambda x}+c \right ) y+c \,x^{n} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
|
| 33 |
\begin{align*}
y^{\prime }&=a \,x^{n} {\mathrm e}^{2 \lambda x} y^{2}+\left (b \,x^{n} {\mathrm e}^{\lambda x}-\lambda \right ) y+c \,x^{n} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 34 |
\begin{align*}
y^{\prime }&=a \,{\mathrm e}^{\lambda x} \left (y-b \,x^{n}-c \right )^{2}+b n \,x^{n -1} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 35 |
\begin{align*}
y^{\prime } x&=a \,{\mathrm e}^{\lambda x} y^{2}+k y+a \,b^{2} x^{2 k} {\mathrm e}^{\lambda x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 36 |
\begin{align*}
y^{\prime } x&=a \,x^{2 n} {\mathrm e}^{\lambda x} y^{2}+\left (b \,x^{n} {\mathrm e}^{\lambda x}-n \right ) y+c \,{\mathrm e}^{\lambda x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 37 |
\begin{align*}
y^{\prime }&=y^{2}+2 a \lambda x \,{\mathrm e}^{\lambda \,x^{2}}-a^{2} {\mathrm e}^{2 \lambda \,x^{2}} \\
\end{align*} |
✓ |
✗ |
✗ |
✗ |
|
| 38 |
\begin{align*}
y^{\prime }&=a \,{\mathrm e}^{-\lambda \,x^{2}} y^{2}+\lambda x y+b^{2} a \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 39 |
\begin{align*}
y^{\prime }&=a \,x^{n} y^{2}+\lambda x y+a \,b^{2} x^{n} {\mathrm e}^{\lambda \,x^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 40 |
\begin{align*}
x^{4} \left (y^{\prime }-y^{2}\right )&=a +b \,{\mathrm e}^{\frac {k}{x}}+c \,{\mathrm e}^{\frac {2 k}{x}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| ID | problem | ODE | Solved? | Maple | Mma | Sympy |
| 1 |
\begin{align*}
y^{\prime }&=y^{2}-a^{2}+a \lambda \sinh \left (\lambda x \right )-a^{2} \sinh \left (\lambda x \right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 2 |
\begin{align*}
y^{\prime }&=y^{2}+a \sinh \left (\beta x \right ) y+a b \sinh \left (\beta x \right )-b^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 3 |
\begin{align*}
y^{\prime }&=y^{2}+a x \sinh \left (b x \right )^{m} y+a \sinh \left (b x \right )^{m} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 4 |
\begin{align*}
y^{\prime }&=\lambda \sinh \left (\lambda x \right ) y^{2}-\lambda \sinh \left (\lambda x \right )^{3} \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
|
| 5 |
\begin{align*}
y^{\prime }&=\left (a \sinh \left (\lambda x \right )^{2}-\lambda \right ) y^{2}-a \sinh \left (\lambda x \right )^{2}+\lambda -a \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 6 |
\begin{align*}
\left (\sinh \left (\lambda x \right ) a +b \right ) y^{\prime }&=y^{2}+c \sinh \left (\mu x \right ) y-d^{2}+c d \sinh \left (\mu x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 7 |
\begin{align*}
\left (\sinh \left (\lambda x \right ) a +b \right ) \left (y^{\prime }-y^{2}\right )+a \,\lambda ^{2} \sinh \left (\lambda x \right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 8 |
\begin{align*}
y^{\prime }&=\alpha y^{2}+\beta +\gamma \cosh \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 9 |
\begin{align*}
y^{\prime }&=y^{2}+a \cosh \left (\beta x \right ) y+a b \cosh \left (\beta x \right )-b^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 10 |
\begin{align*}
y^{\prime }&=y^{2}+a x \cosh \left (b x \right )^{m} y+a \cosh \left (b x \right )^{m} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 11 |
\begin{align*}
y^{\prime }&=\left (a \cosh \left (\lambda x \right )^{2}-\lambda \right ) y^{2}+a +\lambda -a \cosh \left (\lambda x \right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 12 |
\begin{align*}
2 y^{\prime }&=\left (a -\lambda +a \cosh \left (\lambda x \right )\right ) y^{2}+a +\lambda -a \cosh \left (\lambda x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 14 |
\begin{align*}
y^{\prime }&=y^{2} \sinh \left (\lambda x \right ) a +b \sinh \left (\lambda x \right ) \cosh \left (\lambda x \right )^{n} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 15 |
\begin{align*}
y^{\prime }&=a \cosh \left (\lambda x \right ) y^{2}+b \cosh \left (\lambda x \right ) \sinh \left (\lambda x \right )^{n} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
|
| 16 |
\begin{align*}
\left (a \cosh \left (\lambda x \right )+b \right ) y^{\prime }&=y^{2}+c \cosh \left (\mu x \right ) y-d^{2}+c d \cosh \left (\mu x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 17 |
\begin{align*}
\left (a \cosh \left (\lambda x \right )+b \right ) \left (y^{\prime }-y^{2}\right )+a \,\lambda ^{2} \cosh \left (\lambda x \right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| ID | problem | ODE | Solved? | Maple | Mma | Sympy |
| 18 |
\begin{align*}
y^{\prime }&=y^{2}+a \lambda -a \left (a +\lambda \right ) \tanh \left (\lambda x \right )^{2} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
|
| 19 |
\begin{align*}
y^{\prime }&=y^{2}+3 a \lambda -\lambda ^{2}-a \left (a +\lambda \right ) \tanh \left (\lambda x \right )^{2} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
|
| 20 |
\begin{align*}
y^{\prime }&=y^{2}+a x \tanh \left (b x \right )^{m} y+a \tanh \left (b x \right )^{m} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 21 |
\begin{align*}
\left (a \tanh \left (\lambda x \right )+b \right ) y^{\prime }&=y^{2}+c \tanh \left (\mu x \right ) y-d^{2}+c d \tanh \left (\mu x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 22 |
\begin{align*}
y^{\prime }&=y^{2}+a \lambda -a \left (a +\lambda \right ) \coth \left (\lambda x \right )^{2} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
|
| 23 |
\begin{align*}
y^{\prime }&=y^{2}-\lambda ^{2}+3 a \lambda -a \left (a +\lambda \right ) \coth \left (\lambda x \right )^{2} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
|
| 24 |
\begin{align*}
y^{\prime }&=y^{2}+a x \coth \left (b x \right )^{m} y+a \coth \left (b x \right )^{m} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 25 |
\begin{align*}
\left (a \coth \left (\lambda x \right )+b \right ) y^{\prime }&=y^{2}+c \coth \left (\mu x \right ) y-d^{2}+c d \coth \left (\mu x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 26 |
\begin{align*}
y^{\prime }&=y^{2}-2 \lambda ^{2} \tanh \left (\lambda x \right )^{2}-2 \lambda ^{2} \coth \left (\lambda x \right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 27 |
\begin{align*}
y^{\prime }&=y^{2}+a \lambda +b \lambda -2 a b -a \left (a +\lambda \right ) \tanh \left (\lambda x \right )^{2}-b \left (b +\lambda \right ) \coth \left (\lambda x \right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| ID | problem | ODE | Solved? | Maple | Mma | Sympy |
| 1 |
\begin{align*}
y^{\prime }&=a \ln \left (x \right )^{n} y^{2}+b m \,x^{m -1}-a \,b^{2} x^{2 m} \ln \left (x \right )^{n} \\
\end{align*} |
✓ |
✗ |
✗ |
✗ |
|
| 2 |
\begin{align*}
y^{\prime } x&=a y^{2}+b \ln \left (x \right )+c \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 3 |
\begin{align*}
y^{\prime } x&=a y^{2}+b \ln \left (x \right )^{k}+c \ln \left (x \right )^{2 k +2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 4 |
\begin{align*}
y^{\prime } x&=x y^{2}-a^{2} x \ln \left (\beta x \right )^{2}+a \\
\end{align*} |
✓ |
✗ |
✗ |
✗ |
|
| 6 |
\begin{align*}
y^{\prime } x&=a \,x^{n} y^{2}+b -a \,b^{2} x^{n} \ln \left (x \right )^{2} \\
\end{align*} |
✓ |
✗ |
✗ |
✗ |
|
| 7 |
\begin{align*}
x^{2} y^{\prime }&=y^{2} x^{2}+a \ln \left (x \right )^{2}+b \ln \left (x \right )+c \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 9 |
\begin{align*}
x^{2} \ln \left (a x \right ) \left (y^{\prime }-y^{2}\right )&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| ID | problem | ODE | Solved? | Maple | Mma | Sympy |
| 10 |
\begin{align*}
y^{\prime }&=y^{2}+a \ln \left (\beta x \right ) y-a b \ln \left (\beta x \right )-b^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 11 |
\begin{align*}
y^{\prime }&=y^{2}+a x \ln \left (b x \right )^{m} y+a \ln \left (b x \right )^{m} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 12 |
\begin{align*}
y^{\prime }&=a \,x^{n} y^{2}-a b \,x^{n +1} \ln \left (x \right ) y+b \ln \left (x \right )+b \\
\end{align*} |
✓ |
✗ |
✗ |
✗ |
|
| 13 |
\begin{align*}
y^{\prime }&=-\left (n +1\right ) x^{n} y^{2}+a \,x^{n +1} \ln \left (x \right )^{m} y-a \ln \left (x \right )^{m} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 14 |
\begin{align*}
y^{\prime }&=a \ln \left (x \right )^{n} y-a b x \ln \left (x \right )^{n +1} y+b \ln \left (x \right )+b \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 15 |
\begin{align*}
y^{\prime }&=a \ln \left (x \right )^{k} \left (y-b \,x^{n}-c \right )^{2}+b n \,x^{n -1} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 16 |
\begin{align*}
y^{\prime }&=a \ln \left (x \right )^{n} y^{2}+b \ln \left (x \right )^{m} y+b c \ln \left (x \right )^{m}-a \,c^{2} \ln \left (x \right )^{n} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 17 |
\begin{align*}
y^{\prime } x&=\left (a y+b \ln \left (x \right )\right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 18 |
\begin{align*}
y^{\prime } x&=a \ln \left (\lambda x \right )^{m} y^{2}+k y+a \,b^{2} x^{2 k} \ln \left (\lambda x \right )^{m} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 19 |
\begin{align*}
y^{\prime } x&=a \,x^{n} \left (y+b \ln \left (x \right )\right )^{2}-b \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 20 |
\begin{align*}
y^{\prime } x&=a \,x^{2 n} \ln \left (x \right ) y^{2}+\left (b \,x^{n} \ln \left (x \right )-n \right ) y+c \ln \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 21 |
\begin{align*}
x^{2} y^{\prime }&=y^{2} a^{2} x^{2}-y x +b^{2} \ln \left (x \right )^{n} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 22 |
\begin{align*}
\left (a \ln \left (x \right )+b \right ) y^{\prime }&=y^{2}+c \ln \left (x \right )^{n} y-\lambda ^{2}+\lambda c \ln \left (x \right )^{n} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 23 |
\begin{align*}
\left (a \ln \left (x \right )+b \right ) y^{\prime }&=\ln \left (x \right )^{n} y^{2}+c y-\lambda ^{2} \ln \left (x \right )^{n}+\lambda c \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| ID | problem | ODE | Solved? | Maple | Mma | Sympy |
| 1 |
\begin{align*}
y^{\prime }&=\alpha y^{2}+\beta +\gamma \sin \left (\lambda x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 2 |
\begin{align*}
y^{\prime }&=y^{2}-a^{2}+a \lambda \sin \left (\lambda x \right )+a^{2} \sin \left (\lambda x \right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 4 |
\begin{align*}
y^{\prime }&=y^{2}+a \sin \left (\beta x \right ) y+a b \sin \left (\beta x \right )-b^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 6 |
\begin{align*}
y^{\prime }&=\lambda \sin \left (\lambda x \right ) y^{2}+\lambda \sin \left (\lambda x \right )^{3} \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
|
| 7 |
\begin{align*}
2 y^{\prime }&=\left (\lambda +a -\sin \left (\lambda x \right ) a \right ) y^{2}+\lambda -a -\sin \left (\lambda x \right ) a \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
|
| 8 |
\begin{align*}
y^{\prime }&=\left (\lambda +a \sin \left (\lambda x \right )^{2}\right ) y^{2}+\lambda -a +a \sin \left (\lambda x \right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 9 |
\begin{align*}
y^{\prime }&=-\left (1+k \right ) x^{k} y^{2}+a \,x^{1+k} \sin \left (x \right )^{m} y-a \sin \left (x \right )^{m} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 10 |
\begin{align*}
y^{\prime }&=a \sin \left (\lambda x +\mu \right )^{k} \left (y-b \,x^{n}-c \right )^{2}+b n \,x^{n -1} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 11 |
\begin{align*}
y^{\prime } x&=a \sin \left (\lambda x \right )^{m} y^{2}+k y+a \,b^{2} x^{2 k} \sin \left (\lambda x \right )^{m} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 12 |
\begin{align*}
\left (\sin \left (\lambda x \right ) a +b \right ) y^{\prime }&=y^{2}+c \sin \left (\mu x \right ) y-d^{2}+c d \sin \left (\mu x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 13 |
\begin{align*}
\left (\sin \left (\lambda x \right ) a +b \right ) \left (y^{\prime }-y^{2}\right )-a \,\lambda ^{2} \sin \left (\lambda x \right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| ID | problem | ODE | Solved? | Maple | Mma | Sympy |
| 14 |
\begin{align*}
y^{\prime }&=\alpha y^{2}+\beta +\gamma \cos \left (\lambda x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 15 |
\begin{align*}
y^{\prime }&=y^{2}-a^{2}+a \lambda \cos \left (\lambda x \right )+a^{2} \cos \left (\lambda x \right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 17 |
\begin{align*}
y^{\prime }&=y^{2}+a \cos \left (\beta x \right ) y+a b \cos \left (\beta x \right )-b^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 19 |
\begin{align*}
y^{\prime }&=\lambda \cos \left (\lambda x \right ) y^{2}+\lambda \cos \left (\lambda x \right )^{3} \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
|
| 20 |
\begin{align*}
2 y^{\prime }&=\left (\lambda +a -\cos \left (\lambda x \right ) a \right ) y^{2}+\lambda -a -\cos \left (\lambda x \right ) a \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 21 |
\begin{align*}
y^{\prime }&=\left (\lambda +a \cos \left (\lambda x \right )^{2}\right ) y^{2}+\lambda -a +a \cos \left (\lambda x \right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 22 |
\begin{align*}
y^{\prime }&=-\left (1+k \right ) x^{k} y^{2}+a \,x^{1+k} \cos \left (x \right )^{m} y-a \cos \left (x \right )^{m} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 23 |
\begin{align*}
y^{\prime }&=a \cos \left (\lambda x +\mu \right )^{k} \left (y-b \,x^{n}-c \right )^{2}+b n \,x^{n -1} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 24 |
\begin{align*}
y^{\prime } x&=a \cos \left (\lambda x \right )^{m} y^{2}+k y+a \,b^{2} x^{2 k} \cos \left (\lambda x \right )^{m} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 25 |
\begin{align*}
\left (\cos \left (\lambda x \right ) a +b \right ) y^{\prime }&=y^{2}+c \cos \left (\mu x \right ) y-d^{2}+c d \cos \left (\mu x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 26 |
\begin{align*}
\left (\cos \left (\lambda x \right ) a +b \right ) \left (y^{\prime }-y^{2}\right )-a \,\lambda ^{2} \cos \left (\lambda x \right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| ID | problem | ODE | Solved? | Maple | Mma | Sympy |
| 27 |
\begin{align*}
y^{\prime }&=y^{2}+a \lambda +a \left (\lambda -a \right ) \tan \left (\lambda x \right )^{2} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
|
| 28 |
\begin{align*}
y^{\prime }&=y^{2}+\lambda ^{2}+3 a \lambda +a \left (\lambda -a \right ) \tan \left (\lambda x \right )^{2} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
|
| 29 |
\begin{align*}
y^{\prime }&=a y^{2}+b \tan \left (x \right ) y+c \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 30 |
\begin{align*}
y^{\prime }&=a y^{2}+2 a b \tan \left (x \right ) y+b \left (a b -1\right ) \tan \left (x \right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 31 |
\begin{align*}
y^{\prime }&=y^{2}+a \tan \left (\beta x \right ) y+a b \tan \left (\beta x \right )-b^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 32 |
\begin{align*}
y^{\prime }&=y^{2}+a x \tan \left (b x \right )^{m} y+a \tan \left (b x \right )^{m} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 33 |
\begin{align*}
y^{\prime }&=-\left (1+k \right ) x^{k} y^{2}+a \,x^{1+k} \tan \left (x \right )^{m} y-a \tan \left (x \right )^{m} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 34 |
\begin{align*}
y^{\prime }&=a \tan \left (\lambda x \right )^{n} y^{2}-a \,b^{2} \tan \left (\lambda x \right )^{n +2}+b \lambda \tan \left (\lambda x \right )^{2}+b \lambda \\
\end{align*} |
✓ |
✗ |
✗ |
✗ |
|
| 35 |
\begin{align*}
y^{\prime }&=a \tan \left (\lambda x +\mu \right )^{k} \left (y-b \,x^{n}-c \right )^{2}+b n \,x^{n -1} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
|
| 36 |
\begin{align*}
y^{\prime } x&=a \tan \left (\lambda x \right )^{m} y^{2}+k y+a \,b^{2} x^{2 k} \tan \left (\lambda x \right )^{m} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 37 |
\begin{align*}
\left (a \tan \left (\lambda x \right )+b \right ) y^{\prime }&=y^{2}+k \tan \left (\mu x \right ) y-d^{2}+k d \tan \left (\mu x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| ID | problem | ODE | Solved? | Maple | Mma | Sympy |
| 38 |
\begin{align*}
y^{\prime }&=y^{2}+a \lambda +a \left (\lambda -a \right ) \cot \left (\lambda x \right )^{2} \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
|
| 39 |
\begin{align*}
y^{\prime }&=y^{2}+\lambda ^{2}+3 a \lambda +a \left (\lambda -a \right ) \cot \left (\lambda x \right )^{2} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
|
| 40 |
\begin{align*}
y^{\prime }&=y^{2}-2 a b \cot \left (a x \right ) y+b^{2}-a^{2} \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
|
| 41 |
\begin{align*}
y^{\prime }&=y^{2}+a \cot \left (\beta x \right ) y+a b \cot \left (\beta x \right )-b^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 42 |
\begin{align*}
y^{\prime }&=y^{2}+a x \cot \left (b x \right )^{m} y+a \cot \left (b x \right )^{m} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 43 |
\begin{align*}
y^{\prime }&=-\left (1+k \right ) x^{k} y^{2}+a \,x^{1+k} \cot \left (x \right )^{m} y-a \cot \left (x \right )^{m} \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
|
| 44 |
\begin{align*}
y^{\prime }&=a \cot \left (\lambda x +\mu \right )^{k} \left (y-b \,x^{n}-c \right )^{2}+b n \,x^{n -1} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
|
| 45 |
\begin{align*}
y^{\prime } x&=a \cot \left (\lambda x \right )^{m} y^{2}+k y+a \,b^{2} x^{2 k} \cot \left (\lambda x \right )^{m} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 46 |
\begin{align*}
\left (a \cot \left (\lambda x \right )+b \right ) y^{\prime }&=y^{2}+c \cot \left (\mu x \right ) y-d^{2}+c d \cot \left (\mu x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| ID | problem | ODE | Solved? | Maple | Mma | Sympy |
| 48 |
\begin{align*}
y^{\prime }&=\sin \left (\lambda x \right ) a y^{2}+b \sin \left (\lambda x \right ) \cos \left (\lambda x \right )^{n} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 50 |
\begin{align*}
y^{\prime }&=a \cos \left (\lambda x \right ) y^{2}+b \cos \left (\lambda x \right ) \sin \left (\lambda x \right )^{n} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
|
| 51 |
\begin{align*}
y^{\prime }&=\lambda \sin \left (\lambda x \right ) y^{2}+a \,x^{n} \cos \left (\lambda x \right ) y-a \,x^{n} \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
|
| 52 |
\begin{align*}
\sin \left (2 x \right )^{n +1} y^{\prime }&=a y^{2} \sin \left (x \right )^{2 n}+b \cos \left (x \right )^{2 n} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 53 |
\begin{align*}
y^{\prime }&=y^{2}-\tan \left (x \right ) y+a \left (1-a \right ) \cot \left (x \right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 54 |
\begin{align*}
y^{\prime }&=y^{2}-m y \tan \left (x \right )+b^{2} \cos \left (x \right )^{2 m} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 55 |
\begin{align*}
y^{\prime }&=y^{2}+m y \cot \left (x \right )+b^{2} \sin \left (x \right )^{2 m} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 57 |
\begin{align*}
y^{\prime }&=y^{2}+a \lambda +b \lambda +2 a b +a \left (\lambda -a \right ) \tan \left (\lambda x \right )^{2}+b \left (\lambda -b \right ) \cot \left (\lambda x \right )^{2} \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
|
| 58 |
\begin{align*}
y^{\prime }&=y^{2}-\frac {\lambda ^{2}}{2}-\frac {3 \lambda ^{2} \tan \left (\lambda x \right )^{2}}{4}+a \cos \left (\lambda x \right )^{2} \sin \left (\lambda x \right )^{n} \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
|
| 59 |
\begin{align*}
y^{\prime }&=\lambda \sin \left (\lambda x \right ) y^{2}+a \sin \left (\lambda x \right ) y-a \tan \left (\lambda x \right ) \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
|
| ID | problem | ODE | Solved? | Maple | Mma | Sympy |
| 1 |
\begin{align*}
y^{\prime }&=y^{2}+\lambda \arcsin \left (x \right )^{n} y-a^{2}+a \lambda \arcsin \left (x \right )^{n} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 2 |
\begin{align*}
y^{\prime }&=y^{2}+\lambda x \arcsin \left (x \right )^{n} y+\arcsin \left (x \right )^{n} \lambda \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 3 |
\begin{align*}
y^{\prime }&=-\left (1+k \right ) x^{k} y^{2}+\lambda \arcsin \left (x \right )^{n} \left (x^{1+k} y-1\right ) \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
|
| 4 |
\begin{align*}
y^{\prime }&=\lambda \arcsin \left (x \right )^{n} y^{2}+a y+a b -b^{2} \lambda \arcsin \left (x \right )^{n} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 5 |
\begin{align*}
y^{\prime }&=\lambda \arcsin \left (x \right )^{n} y^{2}-b \lambda \,x^{m} \arcsin \left (x \right )^{n} y+b m \,x^{m -1} \\
\end{align*} |
✓ |
✗ |
✗ |
✗ |
|
| 6 |
\begin{align*}
y^{\prime }&=\lambda \arcsin \left (x \right )^{n} y^{2}+\beta m \,x^{m -1}-\lambda \,\beta ^{2} x^{2 m} \arcsin \left (x \right )^{n} \\
\end{align*} |
✓ |
✗ |
✗ |
✗ |
|
| 7 |
\begin{align*}
y^{\prime }&=\lambda \arcsin \left (x \right )^{n} \left (y-a \,x^{m}-b \right )^{2}+a m \,x^{m -1} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
|
| 8 |
\begin{align*}
y^{\prime } x&=\lambda \arcsin \left (x \right )^{n} y^{2}+k y+\lambda \,b^{2} x^{2 k} \arcsin \left (x \right )^{n} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| ID | problem | ODE | Solved? | Maple | Mma | Sympy |
| 10 |
\begin{align*}
y^{\prime }&=y^{2}+\lambda \arccos \left (x \right )^{n} y-a^{2}+a \lambda \arccos \left (x \right )^{n} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 11 |
\begin{align*}
y^{\prime }&=y^{2}+\lambda x \arccos \left (x \right )^{n} y+\arccos \left (x \right )^{n} \lambda \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 12 |
\begin{align*}
y^{\prime }&=-\left (1+k \right ) x^{k} y^{2}+\lambda \arccos \left (x \right )^{n} \left (x^{1+k} y-1\right ) \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
|
| 13 |
\begin{align*}
y^{\prime }&=\lambda \arccos \left (x \right )^{n} y^{2}+a y+a b -b^{2} \lambda \arccos \left (x \right )^{n} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 14 |
\begin{align*}
y^{\prime }&=\lambda \arccos \left (x \right )^{n} y^{2}-b \lambda \,x^{m} \arccos \left (x \right )^{n} y+b m \,x^{m -1} \\
\end{align*} |
✓ |
✗ |
✗ |
✗ |
|
| 15 |
\begin{align*}
y^{\prime }&=\lambda \arccos \left (x \right )^{n} y^{2}+\beta m \,x^{m -1}-\lambda \,\beta ^{2} x^{2 m} \arccos \left (x \right )^{n} \\
\end{align*} |
✓ |
✗ |
✗ |
✗ |
|
| 16 |
\begin{align*}
y^{\prime }&=\lambda \arccos \left (x \right )^{n} \left (y-a \,x^{m}-b \right )^{2}+a m \,x^{m -1} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
|
| 17 |
\begin{align*}
y^{\prime } x&=\lambda \arccos \left (x \right )^{n} y^{2}+k y+\lambda \,b^{2} x^{2 k} \arccos \left (x \right )^{n} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| ID | problem | ODE | Solved? | Maple | Mma | Sympy |
| 19 |
\begin{align*}
y^{\prime }&=y^{2}+\lambda \arctan \left (x \right )^{n} y-a^{2}+a \lambda \arctan \left (x \right )^{n} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 20 |
\begin{align*}
y^{\prime }&=y^{2}+\lambda x \arctan \left (x \right )^{n} y+\arctan \left (x \right )^{n} \lambda \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 21 |
\begin{align*}
y^{\prime }&=-\left (1+k \right ) x^{k} y^{2}+\lambda \arctan \left (x \right )^{n} \left (x^{1+k} y-1\right ) \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
|
| 22 |
\begin{align*}
y^{\prime }&=\lambda \arctan \left (x \right )^{n} y^{2}+a y+a b -b^{2} \lambda \arctan \left (x \right )^{n} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 23 |
\begin{align*}
y^{\prime }&=\lambda \arctan \left (x \right )^{n} y^{2}-b \lambda \,x^{m} \arctan \left (x \right )^{n} y+b m \,x^{m -1} \\
\end{align*} |
✓ |
✗ |
✗ |
✗ |
|
| 25 |
\begin{align*}
y^{\prime }&=\lambda \arctan \left (x \right )^{n} \left (y-a \,x^{m}-b \right )^{2}+a m \,x^{m -1} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
|
| 26 |
\begin{align*}
y^{\prime } x&=\lambda \arctan \left (x \right )^{n} y^{2}+k y+\lambda \,b^{2} x^{2 k} \arctan \left (x \right )^{n} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| ID | problem | ODE | Solved? | Maple | Mma | Sympy |
| 29 |
\begin{align*}
y^{\prime }&=y^{2}+\lambda x \operatorname {arccot}\left (x \right )^{n} y+\operatorname {arccot}\left (x \right )^{n} \lambda \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 30 |
\begin{align*}
y^{\prime }&=-\left (1+k \right ) x^{k} y^{2}+\lambda \operatorname {arccot}\left (x \right )^{n} \left (x^{1+k} y-1\right ) \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
|
| 31 |
\begin{align*}
y^{\prime }&=\lambda \operatorname {arccot}\left (x \right )^{n} y^{2}+a y+a b -b^{2} \lambda \operatorname {arccot}\left (x \right )^{n} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 32 |
\begin{align*}
y^{\prime }&=\lambda \operatorname {arccot}\left (x \right )^{n} y^{2}-b \lambda \,x^{m} \operatorname {arccot}\left (x \right )^{n} y+b m \,x^{m -1} \\
\end{align*} |
✓ |
✗ |
✗ |
✗ |
|
| 34 |
\begin{align*}
y^{\prime }&=\lambda \operatorname {arccot}\left (x \right )^{n} \left (y-a \,x^{m}-b \right )^{2}+a m \,x^{m -1} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
|
| 35 |
\begin{align*}
y^{\prime } x&=\lambda \operatorname {arccot}\left (x \right )^{n} y^{2}+k y+\lambda \,b^{2} x^{2 k} \operatorname {arccot}\left (x \right )^{n} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| ID | problem | ODE | Solved? | Maple | Mma | Sympy |
| 1 |
\begin{align*}
y^{\prime }&=y^{2}+f \left (x \right ) y-a^{2}-a f \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 2 |
\begin{align*}
y^{\prime }&=f \left (x \right ) y^{2}-a y-a b -b^{2} f \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 3 |
\begin{align*}
y^{\prime }&=f \left (x \right )+x f \left (x \right ) y+y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 4 |
\begin{align*}
y^{\prime }&=f \left (x \right ) y^{2}-a \,x^{n} f \left (x \right ) y+x^{n -1} a n \\
\end{align*} |
✓ |
✗ |
✗ |
✗ |
|
| 5 |
\begin{align*}
y^{\prime }&=f \left (x \right ) y^{2}+x^{n -1} a n -a^{2} x^{2 n} f \left (x \right ) \\
\end{align*} |
✓ |
✗ |
✗ |
✗ |
|
| 6 |
\begin{align*}
y^{\prime }&=-\left (n +1\right ) x^{n} y^{2}+x^{n +1} f \left (x \right ) y-f \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
|
| 7 |
\begin{align*}
y^{\prime } x&=f \left (x \right ) y^{2}+n y+a \,x^{2 n} f \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 8 |
\begin{align*}
y^{\prime } x&=x^{2 n} f \left (x \right ) y^{2}+\left (a \,x^{n} f \left (x \right )-n \right ) y+f \left (x \right ) b \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 9 |
\begin{align*}
y^{\prime }&=f \left (x \right ) y^{2}+g \left (x \right ) y-a^{2} f \left (x \right )-a g \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 10 |
\begin{align*}
y^{\prime }&=f \left (x \right ) y^{2}+g \left (x \right ) y+x^{n -1} a n -a \,x^{n} g \left (x \right )-a^{2} x^{2 n} f \left (x \right ) \\
\end{align*} |
✓ |
✗ |
✗ |
✗ |
|
| 11 |
\begin{align*}
y^{\prime }&=f \left (x \right ) y^{2}-a \,x^{n} g \left (x \right ) y+x^{n -1} a n +a^{2} x^{2 n} \left (g \left (x \right )-f \left (x \right )\right ) \\
\end{align*} |
✓ |
✗ |
✗ |
✗ |
|
| 12 |
\begin{align*}
y^{\prime }&=a \,{\mathrm e}^{\lambda x} y^{2}+a \,{\mathrm e}^{\lambda x} f \left (x \right ) y+\lambda f \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 13 |
\begin{align*}
y^{\prime }&=f \left (x \right ) y^{2}-a \,{\mathrm e}^{\lambda x} f \left (x \right ) y+a \lambda \,{\mathrm e}^{\lambda x} \\
\end{align*} |
✓ |
✗ |
✓ |
✗ |
|
| 14 |
\begin{align*}
y^{\prime }&=f \left (x \right ) y^{2}+a \lambda \,{\mathrm e}^{\lambda x}-a^{2} {\mathrm e}^{2 \lambda x} f \left (x \right ) \\
\end{align*} |
✓ |
✗ |
✗ |
✗ |
|
| 15 |
\begin{align*}
y^{\prime }&=f \left (x \right ) y^{2}+\lambda y+a^{2} {\mathrm e}^{2 \lambda x} f \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 16 |
\begin{align*}
y^{\prime }&=f \left (x \right ) y^{2}-f \left (x \right ) \left (a \,{\mathrm e}^{\lambda x}+b \right ) y+a \lambda \,{\mathrm e}^{\lambda x} \\
\end{align*} |
✓ |
✗ |
✗ |
✗ |
|
| 17 |
\begin{align*}
y^{\prime }&={\mathrm e}^{\lambda x} f \left (x \right ) y^{2}+\left (a f \left (x \right )-\lambda \right ) y+b \,{\mathrm e}^{-\lambda x} f \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 18 |
\begin{align*}
y^{\prime }&=f \left (x \right ) y^{2}+g \left (x \right ) y+a \lambda \,{\mathrm e}^{\lambda x}-a \,{\mathrm e}^{\lambda x} g \left (x \right )-a^{2} {\mathrm e}^{2 \lambda x} f \left (x \right ) \\
\end{align*} |
✓ |
✗ |
✗ |
✗ |
|
| 19 |
\begin{align*}
y^{\prime }&=f \left (x \right ) y^{2}-a \,{\mathrm e}^{\lambda x} g \left (x \right ) y+a \lambda \,{\mathrm e}^{\lambda x}+a^{2} {\mathrm e}^{2 \lambda x} \left (g \left (x \right )-f \left (x \right )\right ) \\
\end{align*} |
✓ |
✗ |
✗ |
✗ |
|
| 20 |
\begin{align*}
y^{\prime }&=f \left (x \right ) y^{2}+2 a \lambda x \,{\mathrm e}^{\lambda \,x^{2}}-a^{2} f \left (x \right ) {\mathrm e}^{2 \lambda \,x^{2}} \\
\end{align*} |
✓ |
✗ |
✗ |
✗ |
|
| 22 |
\begin{align*}
y^{\prime }&=f \left (x \right ) y^{2}-a \tanh \left (\lambda x \right )^{2} \left (a f \left (x \right )+\lambda \right )+a \lambda \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
|
| 23 |
\begin{align*}
y^{\prime }&=f \left (x \right ) y^{2}-a \coth \left (\lambda x \right )^{2} \left (a f \left (x \right )+\lambda \right )+a \lambda \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
|
| 24 |
\begin{align*}
y^{\prime }&=f \left (x \right ) y^{2}-a^{2} f \left (x \right )+a \lambda \sinh \left (\lambda x \right )-a^{2} f \left (x \right ) \sinh \left (\lambda x \right )^{2} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
|
| 25 |
\begin{align*}
y^{\prime } x&=f \left (x \right ) y^{2}+a -a^{2} f \left (x \right ) \ln \left (x \right )^{2} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
|
| 26 |
\begin{align*}
y^{\prime } x&=f \left (x \right ) \left (y+a \ln \left (x \right )\right )^{2}-a \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
|
| 27 |
\begin{align*}
y^{\prime }&=f \left (x \right ) y^{2}-a x \ln \left (x \right ) f \left (x \right ) y+a \ln \left (x \right )+a \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
|
| 28 |
\begin{align*}
y^{\prime }&=-a \ln \left (x \right ) y^{2}+a f \left (x \right ) \left (x \ln \left (x \right )-x \right ) y-f \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
|
| 29 |
\begin{align*}
y^{\prime }&=\lambda \sin \left (\lambda x \right ) y^{2}+f \left (x \right ) \cos \left (\lambda x \right ) y-f \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
|
| 30 |
\begin{align*}
y^{\prime }&=f \left (x \right ) y^{2}-a^{2} f \left (x \right )+a \lambda \sin \left (\lambda x \right )+a^{2} f \left (x \right ) \sin \left (\lambda x \right )^{2} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
|
| 31 |
\begin{align*}
y^{\prime }&=f \left (x \right ) y^{2}-a^{2} f \left (x \right )+a \lambda \cos \left (\lambda x \right )+a^{2} f \left (x \right ) \cos \left (\lambda x \right )^{2} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
|
| 32 |
\begin{align*}
y^{\prime }&=f \left (x \right ) y^{2}-a \tan \left (\lambda x \right )^{2} \left (a f \left (x \right )-\lambda \right )+a \lambda \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
|
| 33 |
\begin{align*}
y^{\prime }&=f \left (x \right ) y^{2}-a \cot \left (\lambda x \right )^{2} \left (a f \left (x \right )-\lambda \right )+a \lambda \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
|
| ID | problem | ODE | Solved? | Maple | Mma | Sympy |
| 34 |
\begin{align*}
y^{\prime }&=y^{2}-f \left (x \right )^{2}+f^{\prime }\left (x \right ) \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
|
| 35 |
\begin{align*}
y^{\prime }&=f \left (x \right ) y^{2}-f \left (x \right ) g \left (x \right ) y+g^{\prime }\left (x \right ) \\
\end{align*} |
✓ |
✗ |
✗ |
✗ |
|
| 36 |
\begin{align*}
y^{\prime }&=-f^{\prime }\left (x \right ) y^{2}+f \left (x \right ) g \left (x \right ) y-g \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
|
| 37 |
\begin{align*}
y^{\prime }&=g \left (x \right ) \left (y-f \left (x \right )\right )^{2}+f^{\prime }\left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 38 |
\begin{align*}
y^{\prime }&=\frac {y^{2} f^{\prime }\left (x \right )}{g \left (x \right )}-\frac {g^{\prime }\left (x \right )}{f \left (x \right )} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
|
| 39 |
\begin{align*}
f \left (x \right )^{2} y^{\prime }-f^{\prime }\left (x \right ) y^{2}+g \left (x \right ) \left (y-f \left (x \right )\right )&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
|
| 40 |
\begin{align*}
y^{\prime }&=f^{\prime }\left (x \right ) y^{2}+a \,{\mathrm e}^{\lambda x} f \left (x \right ) y+a \,{\mathrm e}^{\lambda x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 41 |
\begin{align*}
y^{\prime }&=f \left (x \right ) y^{2}+g^{\prime }\left (x \right ) y+a f \left (x \right ) {\mathrm e}^{2 g \left (x \right )} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 42 |
\begin{align*}
y^{\prime }&=y^{2}-\frac {f^{\prime \prime }\left (x \right )}{f \left (x \right )} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| ID | problem | ODE | Solved? | Maple | Mma | Sympy |
| 1 |
\begin{align*}
y^{\prime }&=y^{2}+a^{2} f \left (a x +b \right ) \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
|
| 2 |
\begin{align*}
y^{\prime }&=y^{2}+\frac {f \left (\frac {1}{x}\right )}{x^{4}} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
|
| 4 |
\begin{align*}
x^{2} y^{\prime }&=x^{4} f \left (x \right ) y^{2}+1 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
|
| 5 |
\begin{align*}
x^{2} y^{\prime }&=y^{2} x^{4}+x^{2 n} f \left (a \,x^{n}+b \right )-\frac {n^{2}}{4}+\frac {1}{4} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
|
| 6 |
\begin{align*}
y^{\prime }&=f \left (x \right ) y^{2}+g \left (x \right ) y+h \left (x \right ) \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
|
| 11 |
\begin{align*}
x^{2} y^{\prime }&=y^{2} x^{2}+f \left (a \ln \left (x \right )+b \right )+\frac {1}{4} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
|
| ID | problem | ODE | Solved? | Maple | Mma | Sympy |
| 1 |
\begin{align*}
y y^{\prime }-y&=A \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 2 |
\begin{align*}
y y^{\prime }-y&=A x +B \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 3 |
\begin{align*}
y y^{\prime }-y&=-\frac {2 x}{9}+A +\frac {B}{\sqrt {x}} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
|
| 4 |
\begin{align*}
y y^{\prime }-y&=2 A \left (\sqrt {x}+4 A +\frac {3 A^{2}}{\sqrt {x}}\right ) \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
|
| 5 |
\begin{align*}
y y^{\prime }-y&=A x +\frac {B}{x}-\frac {B^{2}}{x^{3}} \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
|
| 7 |
\begin{align*}
y y^{\prime }-y&=\frac {A}{x}-\frac {A^{2}}{x^{3}} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
|
| 8 |
\begin{align*}
y y^{\prime }-y&=A +B \,{\mathrm e}^{-\frac {2 x}{A}} \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
|
| 9 |
\begin{align*}
y y^{\prime }-y&=A \left ({\mathrm e}^{\frac {2 x}{A}}-1\right ) \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
|
| 11 |
\begin{align*}
y y^{\prime }-y&=-\frac {2 x}{9}+6 A^{2} \left (1+\frac {2 A}{\sqrt {x}}\right ) \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
|
| 13 |
\begin{align*}
y y^{\prime }-y&=\frac {\left (2 m +1\right ) x}{4 m^{2}}+\frac {A}{x}-\frac {A^{2}}{x^{3}} \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
|
| 14 |
\begin{align*}
y y^{\prime }-y&=\frac {4}{9} x +2 A \,x^{2}+2 A^{2} x^{3} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
|
| 15 |
\begin{align*}
y y^{\prime }-y&=-\frac {3 x}{16}+\frac {5 A}{x^{{1}/{3}}}-\frac {12 A^{2}}{x^{{5}/{3}}} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
|
| 16 |
\begin{align*}
y y^{\prime }-y&=\frac {A}{x} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
|
| 17 |
\begin{align*}
y y^{\prime }-y&=-\frac {x}{4}+\frac {A \left (\sqrt {x}+5 A +\frac {3 A^{2}}{\sqrt {x}}\right )}{4} \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
|
| 18 |
\begin{align*}
y y^{\prime }-y&=\frac {2 a^{2}}{\sqrt {8 a^{2}+x^{2}}} \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
|
| 19 |
\begin{align*}
y y^{\prime }-y&=2 x +\frac {A}{x^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 21 |
\begin{align*}
y y^{\prime }-y&=\frac {3 x}{8}+\frac {3 \sqrt {a^{2}+x^{2}}}{8}-\frac {a^{2}}{16 \sqrt {a^{2}+x^{2}}} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
|
| 22 |
\begin{align*}
y y^{\prime }-y&=-\frac {4 x}{25}+\frac {A}{\sqrt {x}} \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
|
| 23 |
\begin{align*}
y y^{\prime }-y&=-\frac {9 x}{100}+\frac {A}{x^{{5}/{3}}} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
|
| 24 |
\begin{align*}
y y^{\prime }-y&=-\frac {12 x}{49}+\frac {2 A \left (5 \sqrt {x}+34 A +\frac {15 A^{2}}{\sqrt {x}}\right )}{49} \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
|
| 25 |
\begin{align*}
y y^{\prime }-y&=-\frac {12 x}{49}+\frac {A \left (25 \sqrt {x}+41 A +\frac {10 A^{2}}{\sqrt {x}}\right )}{98} \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
|
| 26 |
\begin{align*}
y y^{\prime }-y&=-\frac {2 x}{9}+\frac {A}{\sqrt {x}} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
|
| 28 |
\begin{align*}
y y^{\prime }-y&=-\frac {12 x}{49}+\frac {6 A \left (-3 \sqrt {x}+23 A +\frac {12 A^{2}}{\sqrt {x}}\right )}{49} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
|
| 29 |
\begin{align*}
y y^{\prime }-y&=-\frac {30 x}{121}+\frac {3 A \left (21 \sqrt {x}+35 A +\frac {6 A^{2}}{\sqrt {x}}\right )}{242} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
|
| 30 |
\begin{align*}
y y^{\prime }-y&=-\frac {3 x}{16}+\frac {A}{x^{{5}/{3}}} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
|
| 31 |
\begin{align*}
y y^{\prime }-y&=-\frac {12 x}{49}+\frac {4 A \left (-10 \sqrt {x}+27 A +\frac {10 A^{2}}{\sqrt {x}}\right )}{49} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
|
| 32 |
\begin{align*}
y y^{\prime }-y&=\frac {A}{\sqrt {x}} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
|
| 33 |
\begin{align*}
y y^{\prime }-y&=\frac {A}{x^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 34 |
\begin{align*}
y y^{\prime }-y&=A \left (n +2\right ) \left (\sqrt {x}+2 \left (n +2\right ) A +\frac {\left (n +1\right ) \left (n +3\right ) A^{2}}{\sqrt {x}}\right ) \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
|
| 35 |
\begin{align*}
y y^{\prime }-y&=A \left (n +2\right ) \left (\sqrt {x}+2 \left (n +2\right ) A +\frac {\left (2 n +3\right ) A^{2}}{\sqrt {x}}\right ) \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
|
| 36 |
\begin{align*}
y y^{\prime }-y&=A \sqrt {x}+2 A^{2}+\frac {B}{\sqrt {x}} \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
|
| 37 |
\begin{align*}
y y^{\prime }-y&=2 A^{2}-A \sqrt {x} \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
|
| 38 |
\begin{align*}
y y^{\prime }-y&=-\frac {x}{4}+\frac {6 A \left (\sqrt {x}+8 A +\frac {5 A^{2}}{\sqrt {x}}\right )}{49} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
|
| 39 |
\begin{align*}
y y^{\prime }-y&=-\frac {6 x}{25}+\frac {6 A \left (2 \sqrt {x}+7 A +\frac {4 A^{2}}{\sqrt {x}}\right )}{25} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
|
| 40 |
\begin{align*}
y y^{\prime }-y&=-\frac {3 x}{16}+\frac {3 A}{x^{{1}/{3}}}-\frac {12 A^{2}}{x^{{5}/{3}}} \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
|
| 42 |
\begin{align*}
y y^{\prime }-y&=\frac {9 x}{32}+\frac {15 \sqrt {b^{2}+x^{2}}}{32}+\frac {3 b^{2}}{64 \sqrt {b^{2}+x^{2}}} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
|
| 44 |
\begin{align*}
y y^{\prime }-y&=A \,x^{2}-\frac {9}{625 A} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
|
| 45 |
\begin{align*}
y y^{\prime }-y&=-\frac {6}{25} x -A \,x^{2} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
|
| 46 |
\begin{align*}
y y^{\prime }-y&=\frac {6}{25} x -A \,x^{2} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
|
| 47 |
\begin{align*}
y y^{\prime }-y&=12 x +\frac {A}{x^{{5}/{2}}} \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
|
| 48 |
\begin{align*}
y y^{\prime }-y&=\frac {63 x}{4}+\frac {A}{x^{{5}/{3}}} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
|
| 49 |
\begin{align*}
y y^{\prime }-y&=2 x +2 A \left (10 \sqrt {x}+31 A +\frac {30 A^{2}}{\sqrt {x}}\right ) \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
|
| 50 |
\begin{align*}
y y^{\prime }-y&=2 x +2 A \left (-10 \sqrt {x}+19 A +\frac {30 A^{2}}{\sqrt {x}}\right ) \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
|
| 52 |
\begin{align*}
y y^{\prime }-y&=-\frac {12 x}{49}+\frac {A \left (5 \sqrt {x}+262 A +\frac {65 A^{2}}{\sqrt {x}}\right )}{49} \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
|
| 53 |
\begin{align*}
y y^{\prime }-y&=-\frac {12 x}{49}+A \sqrt {x} \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
|
| 54 |
\begin{align*}
y y^{\prime }-y&=6 x +\frac {A}{x^{4}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 55 |
\begin{align*}
y y^{\prime }-y&=20 x +\frac {A}{\sqrt {x}} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
|
| 56 |
\begin{align*}
y y^{\prime }-y&=\frac {15 x}{4}+\frac {A}{x^{7}} \\
\end{align*} |
✓ |
✗ |
✗ |
✗ |
|
| 57 |
\begin{align*}
y y^{\prime }-y&=-\frac {10 x}{49}+\frac {2 A \left (4 \sqrt {x}+61 A +\frac {12 A^{2}}{\sqrt {x}}\right )}{49} \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
|
| 58 |
\begin{align*}
y y^{\prime }-y&=-\frac {12 x}{49}+\frac {2 A \left (\sqrt {x}+166 A +\frac {55 A^{2}}{\sqrt {x}}\right )}{49} \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
|
| 59 |
\begin{align*}
y y^{\prime }-y&=-\frac {4 x}{25}+\frac {A \left (7 \sqrt {x}+49 A +\frac {6 A^{2}}{\sqrt {x}}\right )}{50} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
|
| 60 |
\begin{align*}
y y^{\prime }-y&=\frac {15 x}{4}+\frac {6 A}{x^{{1}/{3}}}-\frac {3 A^{2}}{x^{{5}/{3}}} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
|
| 61 |
\begin{align*}
y y^{\prime }-y&=-\frac {3 x}{16}+\frac {A}{x^{{1}/{3}}}+\frac {B}{x^{{5}/{3}}} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
|
| 63 |
\begin{align*}
y y^{\prime }-y&=\frac {k}{\sqrt {A \,x^{2}+B x +c}} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
|
| 65 |
\begin{align*}
y y^{\prime }-y&=-\frac {6 x}{25}+\frac {4 B^{2} \left (\left (2-A \right ) x^{{1}/{3}}-\frac {3 B \left (2 A +1\right )}{2}+\frac {B^{2} \left (1-3 A \right )}{x^{{1}/{3}}}-\frac {A \,B^{3}}{x^{{2}/{3}}}\right )}{75} \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
|
| 71 |
\begin{align*}
y y^{\prime }-y&=a x +b \,x^{m} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
|
| 73 |
\begin{align*}
y y^{\prime }-y&=a^{2} \lambda \,{\mathrm e}^{2 \lambda x}-a \left (b \lambda +1\right ) {\mathrm e}^{\lambda x}+b \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
|
| 76 |
\begin{align*}
y y^{\prime }-y&=a^{2} f^{\prime }\left (x \right ) f^{\prime \prime }\left (x \right )-\frac {\left (f \left (x \right )+b \right )^{2} f^{\prime \prime }\left (x \right )}{{f^{\prime }\left (x \right )}^{3}} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
|
| ID | problem | ODE | Solved? | Maple | Mma | Sympy |
| 1 |
\begin{align*}
y y^{\prime }&=\left (a x +b \right ) y+1 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
|
| 2 |
\begin{align*}
y y^{\prime }&=\frac {y}{\left (a x +b \right )^{2}}+1 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
|
| 3 |
\begin{align*}
y y^{\prime }&=\left (a -\frac {1}{a x}\right ) y+1 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
|
| 4 |
\begin{align*}
y y^{\prime }&=\frac {y}{\sqrt {a x +b}}+1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 5 |
\begin{align*}
y y^{\prime }&=\frac {3 y}{\sqrt {a \,x^{{3}/{2}}+8 x}}+1 \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
|
| 6 |
\begin{align*}
y y^{\prime }&=\left (\frac {a}{x^{{2}/{3}}}-\frac {2}{3 a \,x^{{1}/{3}}}\right ) y+1 \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
|
| 7 |
\begin{align*}
y y^{\prime }&=a \,{\mathrm e}^{\lambda x} y+1 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
|
| 8 |
\begin{align*}
y y^{\prime }&=\left (a \,{\mathrm e}^{\lambda x}+b \,{\mathrm e}^{-\lambda x}\right ) y+1 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
|
| 9 |
\begin{align*}
y y^{\prime }&=a y \cosh \left (x \right )+1 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
|
| 11 |
\begin{align*}
y y^{\prime }&=a \cos \left (\lambda x \right ) y+1 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
|
| 12 |
\begin{align*}
y y^{\prime }&=a \sin \left (\lambda x \right ) y+1 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
|
| ID | problem | ODE | Solved? | Maple | Mma | Sympy |
| 1 |
\begin{align*}
y y^{\prime }&=\left (a x +3 b \right ) y+c \,x^{3}-b \,x^{2} a -2 b^{2} x \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
|
| 2 |
\begin{align*}
y y^{\prime }&=\left (3 a x +b \right ) y-a^{2} x^{3}-b \,x^{2} a +c x \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 3 |
\begin{align*}
2 y y^{\prime }&=\left (7 a x +5 b \right ) y-3 a^{2} x^{3}-2 c \,x^{2}-3 b^{2} x \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
|
| 4 |
\begin{align*}
y y^{\prime }&=\left (\left (3-m \right ) x -1\right ) y-\left (m -1\right ) a x \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
|
| 5 |
\begin{align*}
y y^{\prime }+x \left (a \,x^{2}+b \right ) y+x&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
|
| 6 |
\begin{align*}
y y^{\prime }+a \left (1-\frac {1}{x}\right ) y&=a^{2} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
|
| 7 |
\begin{align*}
y y^{\prime }-a \left (1-\frac {b}{x}\right ) y&=a^{2} b \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
|
| 8 |
\begin{align*}
y y^{\prime }&=x^{n -1} \left (\left (2 n +1\right ) x +a n \right ) y-n \,x^{2 n} \left (a +x \right ) \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
|
| 9 |
\begin{align*}
y y^{\prime }&=a \left (-b n +x \right ) x^{n -1} y+c \left (x^{2}-\left (2 n +1\right ) b x +n \left (n +1\right ) b^{2}\right ) x^{2 n -1} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
|
| 15 |
\begin{align*}
y y^{\prime }-\frac {a \left (x \left (m -1\right )+1\right ) y}{x}&=\frac {a^{2} \left (x m +1\right ) \left (x -1\right )}{x} \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
|
| 16 |
\begin{align*}
y y^{\prime }-a \left (1-\frac {b}{\sqrt {x}}\right ) y&=\frac {a^{2} b}{\sqrt {x}} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
|
| 17 |
\begin{align*}
y y^{\prime }&=\frac {3 y}{\left (a x +b \right )^{{1}/{3}} x^{{5}/{3}}}+\frac {3}{\left (a x +b \right )^{{2}/{3}} x^{{7}/{3}}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 19 |
\begin{align*}
y y^{\prime }+\frac {a \left (6 x -1\right ) y}{2 x}&=-\frac {a^{2} \left (x -1\right ) \left (4 x -1\right )}{2 x} \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
|
| 20 |
\begin{align*}
y y^{\prime }-\frac {a \left (1+\frac {2 b}{x^{2}}\right ) y}{2}&=\frac {a^{2} \left (3 x +\frac {4 b}{x}\right )}{16} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
|
| 24 |
\begin{align*}
y y^{\prime }+\frac {a \left (13 x -18\right ) y}{15 x^{{7}/{5}}}&=-\frac {4 a^{2} \left (x -1\right ) \left (x -6\right )}{15 x^{{9}/{5}}} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
|
| 25 |
\begin{align*}
y y^{\prime }+\frac {a \left (5 x +1\right ) y}{2 \sqrt {x}}&=a^{2} \left (-x^{2}+1\right ) \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
|
| 28 |
\begin{align*}
y y^{\prime }+\frac {a \left (7 x -12\right ) y}{10 x^{{7}/{5}}}&=-\frac {a^{2} \left (x -1\right ) \left (x -16\right )}{10 x^{{9}/{5}}} \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
|
| 29 |
\begin{align*}
y y^{\prime }+\frac {3 a \left (13 x -8\right ) y}{20 x^{{7}/{5}}}&=-\frac {a^{2} \left (x -1\right ) \left (27 x -32\right )}{20 x^{{9}/{5}}} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
|
| 31 |
\begin{align*}
y y^{\prime }-\frac {a \left (x +1\right ) y}{2 x^{{7}/{4}}}&=\frac {a^{2} \left (x -1\right ) \left (3 x +5\right )}{4 x^{{5}/{2}}} \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
|
| 33 |
\begin{align*}
y y^{\prime }-\frac {a \left (4 x +3\right ) y}{14 x^{{8}/{7}}}&=-\frac {a^{2} \left (x -1\right ) \left (16 x +5\right )}{14 x^{{9}/{7}}} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
|
| 34 |
\begin{align*}
y y^{\prime }+\frac {a \left (13 x -3\right ) y}{6 x^{{2}/{3}}}&=-\frac {a^{2} \left (x -1\right ) \left (5 x -1\right )}{6 x^{{1}/{3}}} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
|
| 36 |
\begin{align*}
y y^{\prime }-\frac {a \left (5 x -4\right ) y}{x^{4}}&=\frac {a^{2} \left (x -1\right ) \left (3 x -1\right )}{x^{7}} \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
|
| 37 |
\begin{align*}
y y^{\prime }-\frac {2 a \left (3 x -10\right ) y}{5 x^{4}}&=\frac {a^{2} \left (x -1\right ) \left (8 x -5\right )}{5 x^{7}} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
|
| 38 |
\begin{align*}
y y^{\prime }+\frac {a \left (39 x -4\right ) y}{42 x^{{9}/{7}}}&=-\frac {a^{2} \left (x -1\right ) \left (9 x -1\right )}{42 x^{{11}/{7}}} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
|
| 39 |
\begin{align*}
y y^{\prime }+\frac {a \left (x -2\right ) y}{x}&=\frac {2 a^{2} \left (x -1\right )}{x} \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
|
| 40 |
\begin{align*}
y y^{\prime }+\frac {a \left (3 x -2\right ) y}{x}&=-\frac {2 a^{2} \left (x -1\right )^{2}}{x} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
|
| 41 |
\begin{align*}
y y^{\prime }+\frac {a \left (1-\frac {b}{x^{2}}\right ) y}{x}&=\frac {a^{2} b}{x} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
|
| 42 |
\begin{align*}
y y^{\prime }-\frac {a \left (3 x -4\right ) y}{4 x^{{5}/{2}}}&=\frac {a^{2} \left (x -1\right ) \left (2+x \right )}{4 x^{4}} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
|
| 43 |
\begin{align*}
y y^{\prime }+\frac {a \left (33 x +2\right ) y}{30 x^{{6}/{5}}}&=-\frac {a^{2} \left (x -1\right ) \left (9 x -4\right )}{30 x^{{7}/{5}}} \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
|
| 44 |
\begin{align*}
y y^{\prime }-\frac {a \left (x -8\right ) y}{8 x^{{5}/{2}}}&=-\frac {a^{2} \left (x -1\right ) \left (3 x -4\right )}{8 x^{4}} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
|
| 46 |
\begin{align*}
y y^{\prime }-\frac {a \left (6 x -13\right ) y}{13 x^{{5}/{2}}}&=-\frac {a^{2} \left (x -1\right ) \left (x -13\right )}{26 x^{4}} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
|
| 48 |
\begin{align*}
y y^{\prime }-\frac {2 a \left (3 x +2\right ) y}{5 x^{{8}/{5}}}&=\frac {a^{2} \left (x -1\right ) \left (8 x +1\right )}{5 x^{{11}/{5}}} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
|
| 49 |
\begin{align*}
y y^{\prime }-\frac {6 a \left (4 x +1\right ) y}{5 x^{{7}/{5}}}&=\frac {a^{2} \left (x -1\right ) \left (27 x +8\right )}{5 x^{{9}/{5}}} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
|
| 50 |
\begin{align*}
y y^{\prime }-\frac {a \left (x +4\right ) y}{5 x^{{8}/{5}}}&=\frac {a^{2} \left (x -1\right ) \left (3 x +7\right )}{5 x^{{3}/{5}}} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
|
| 51 |
\begin{align*}
y y^{\prime }-\frac {a \left (x +4\right ) y}{5 x^{{8}/{5}}}&=\frac {a^{2} \left (x -1\right ) \left (3 x +7\right )}{5 x^{{11}/{5}}} \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
|
| 52 |
\begin{align*}
y y^{\prime }-\frac {a \left (2 x -1\right ) y}{x^{{5}/{2}}}&=\frac {a^{2} \left (x -1\right ) \left (1+3 x \right )}{2 x^{4}} \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
|
| 53 |
\begin{align*}
y y^{\prime }+\frac {a \left (x -6\right ) y}{5 x^{{7}/{5}}}&=\frac {2 a^{2} \left (x -1\right ) \left (x +4\right )}{5 x^{{9}/{5}}} \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
|
| 55 |
\begin{align*}
y y^{\prime }-\frac {3 a y}{x^{{7}/{4}}}&=\frac {a^{2} \left (x -1\right ) \left (x -9\right )}{4 x^{{5}/{2}}} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
|
| 56 |
\begin{align*}
y y^{\prime }-\frac {a \left (\left (1+k \right ) x -1\right ) y}{x^{2}}&=\frac {a^{2} \left (1+k \right ) \left (x -1\right )}{x^{2}} \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
|
| 59 |
\begin{align*}
y y^{\prime }-\left (\left (2 n -1\right ) x -a n \right ) x^{-1-n} y&=n \left (x -a \right ) x^{-2 n} \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
|
| 66 |
\begin{align*}
y y^{\prime }-a \left (\frac {n +2}{n}+b \,x^{n}\right ) y&=-\frac {a^{2} x \left (\frac {n +1}{n}+b \,x^{n}\right )}{n} \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
|
| 67 |
\begin{align*}
y y^{\prime }&=\left (a \,{\mathrm e}^{x}+b \right ) y+c \,{\mathrm e}^{2 x}-a b \,{\mathrm e}^{x}-b^{2} \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
|
| 69 |
\begin{align*}
y y^{\prime }&=\left (a \,{\mathrm e}^{\lambda x}+b \right ) y+c \left (a^{2} {\mathrm e}^{2 \lambda x}+a b \left (\lambda x +1\right ) {\mathrm e}^{\lambda x}+b^{2} \lambda x \right ) \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
|
| 70 |
\begin{align*}
y y^{\prime }&={\mathrm e}^{\lambda x} \left (2 a \lambda x +a +b \right ) y-{\mathrm e}^{2 \lambda x} \left (a^{2} \lambda \,x^{2}+a b x +c \right ) \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
|
| 71 |
\begin{align*}
y y^{\prime }&={\mathrm e}^{a x} \left (2 a \,x^{2}+b +2 x \right ) y+{\mathrm e}^{2 a x} \left (-a \,x^{4}-b \,x^{2}+c \right ) \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
|
| 72 |
\begin{align*}
y y^{\prime }+a \left (2 b x +1\right ) {\mathrm e}^{b x} y&=-a^{2} b \,x^{2} {\mathrm e}^{2 b x} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
|
| 73 |
\begin{align*}
y y^{\prime }-a \left (1+2 n +2 n \left (n +1\right ) x \right ) {\mathrm e}^{\left (n +1\right ) x} y&=-a^{2} n \left (n +1\right ) \left (x n +1\right ) x \,{\mathrm e}^{2 \left (n +1\right ) x} \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
|
| 74 |
\begin{align*}
y y^{\prime }+a \left (1+2 b \sqrt {x}\right ) {\mathrm e}^{2 b \sqrt {x}} y&=-a^{2} b \,x^{{3}/{2}} {\mathrm e}^{4 b \sqrt {x}} \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
|
| 77 |
\begin{align*}
y y^{\prime }&=\left (2 \ln \left (x \right )+a +1\right ) y+x \left (-\ln \left (x \right )^{2}-a \ln \left (x \right )+b \right ) \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
|
| 78 |
\begin{align*}
y y^{\prime }&=\left (2 \ln \left (x \right )^{2}+2 \ln \left (x \right )+a \right ) y+x \left (-\ln \left (x \right )^{4}-a \ln \left (x \right )^{2}+b \right ) \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
|
| 79 |
\begin{align*}
y y^{\prime }&=a x \cos \left (\lambda \,x^{2}\right ) y+x \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
|
| ID | problem | ODE | Solved? | Maple | Mma | Sympy |
| 1 |
\begin{align*}
\left (A y+B x +a \right ) y^{\prime }+B y+x k +b&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 2 |
\begin{align*}
\left (y+a x +b \right ) y^{\prime }&=\alpha y+\beta x +\gamma \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
|
| 4 |
\begin{align*}
\left (y+A \,x^{n}+a \right ) y^{\prime }+n A \,x^{n -1} y+k \,x^{m}+b&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 6 |
\begin{align*}
y y^{\prime } x&=a y^{2}+b y+c \,x^{n}+s \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
|
| 7 |
\begin{align*}
y y^{\prime } x&=-n y^{2}+a \left (2 n +1\right ) x y+b y-a^{2} n \,x^{2}-a b x +c \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
|
| 8 |
\begin{align*}
2 y y^{\prime } x&=\left (1-n \right ) y^{2}+\left (a \left (2 n +1\right ) x +2 n -1\right ) y-a^{2} n \,x^{2}-b x -n \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
|
| 9 |
\begin{align*}
\left (a x y-a k y+b x -b k \right ) y^{\prime }&=c y^{2}+d x y+\left (-d k +b \right ) y \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
|
| 14 |
\begin{align*}
x \left (2 a y+b x \right ) y^{\prime }&=a \left (2-m \right ) y^{2}+b \left (1-m \right ) x y+c \,x^{2}+A \,x^{m +2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 15 |
\begin{align*}
\left (x^{2}+y x +a \right ) y^{\prime }&=y^{2}+y x +b \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 16 |
\begin{align*}
\left (2 A x y+B \,x^{2}+b \right ) y^{\prime }&=A y^{2}+k \left (A k +B \right ) x^{2}+c \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 18 |
\begin{align*}
\left (A x y+B \,x^{2}+x k \right ) y^{\prime }&=A y^{2}+B x y+\left (A b +k \right ) y+B b x +b k \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 20 |
\begin{align*}
\left (A x y+B \,x^{2}+x k \right ) y^{\prime }&=A y^{2}+c x y+d \,x^{2}+\left (-A \beta +k \right ) y-c \beta x -k \beta \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
|
| 21 |
\begin{align*}
\left (A x y+A k y+B \,x^{2}+B k x \right ) y^{\prime }&=c y^{2}+d x y+k \left (d -B \right ) y \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
|
| 28 |
\begin{align*}
\left (A x y+B \,x^{2}+\left (-1+k \right ) A a y-\left (A b k +B a \right ) x \right ) y^{\prime }&=A y^{2}+B x y-\left (B a k +A b \right ) y+\left (-1+k \right ) B b x \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 29 |
\begin{align*}
\left (\left (a x +c \right ) y+\left (1-n \right ) x^{2}+\left (2 n -1\right ) x -n \right ) y^{\prime }&=2 a y^{2}+2 y x \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
|
| 31 |
\begin{align*}
x \left (2 a x y+b \right ) y^{\prime }&=-a \left (m +3\right ) x y^{2}-b \left (m +2\right ) y+c \,x^{m} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 34 |
\begin{align*}
x \left (\left (m -1\right ) \left (A x +B \right ) y+m \left (d \,x^{2}+e x +F \right )\right ) y^{\prime }&=\left (A \left (1-n \right ) x -B n \right ) y^{2}+\left (d \left (2-n \right ) x^{2}+e \left (1-n \right ) x -F n \right ) y \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
|
| 35 |
\begin{align*}
x \left (2 a x y+b \right ) y^{\prime }&=-4 a \,x^{2} y^{2}-3 b x y+c \,x^{2}+k \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
|
| 36 |
\begin{align*}
\left (y x +a \,x^{n}+b \,x^{2}\right ) y^{\prime }&=y^{2}+c \,x^{n}+b x y \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
|
| 37 |
\begin{align*}
x \left (2 a \,x^{n} y+b \right ) y^{\prime }&=-a \left (3 n +m \right ) x^{n} y^{2}-b \left (2 n +m \right ) y+A \,x^{m}+x \,x^{-n} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 38 |
\begin{align*}
y y^{\prime }&=-n y^{2}+a \left (2 n +1\right ) {\mathrm e}^{x} y+b y-a^{2} n \,{\mathrm e}^{2 x}-a b \,{\mathrm e}^{x}+c \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
|
| ID | problem | ODE | Solved? | Maple | Mma | Sympy |
| 1 |
\begin{align*}
y^{\prime }&=a y^{3}+\frac {b}{x^{{3}/{2}}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 2 |
\begin{align*}
y^{\prime }&=-y^{3}+3 y a^{2} x^{2}-2 a^{3} x^{3}+a \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
|
| 3 |
\begin{align*}
y^{\prime }&=-y^{3}+\left (a x +b \right ) y^{2} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
|
| 4 |
\begin{align*}
y^{\prime }&=-y^{3}+\frac {y^{2}}{\left (a x +b \right )^{2}} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
|
| 5 |
\begin{align*}
y^{\prime }&=-y^{3}+\frac {y^{2}}{\sqrt {a x +b}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 6 |
\begin{align*}
y^{\prime }&=a y^{3}+3 a b x y^{2}-b -2 a \,b^{3} x^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 7 |
\begin{align*}
y^{\prime }&=a y^{3} x +b y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 8 |
\begin{align*}
y^{\prime }&=a y^{3} x +2 a b \,x^{2} y^{2}-b -2 a \,b^{3} x^{4} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
|
| 9 |
\begin{align*}
y^{\prime }&=a \,x^{2 n +1} y^{3}+b \,x^{-n -2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 10 |
\begin{align*}
y^{\prime }&=a \,x^{n} y^{3}+3 a b \,x^{n +m} y^{2}-b m \,x^{m -1}-2 a \,b^{3} x^{n +3 m} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 11 |
\begin{align*}
y^{\prime }&=a \,x^{n} y^{3}+3 a b \,x^{n +m} y^{2}+c \,x^{k} y-2 a \,b^{3} x^{n +3 m}+b c \,x^{m +k}-b m \,x^{m -1} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 12 |
\begin{align*}
9 y^{\prime }&=-x^{m} \left (a \,x^{1-m}+b \right )^{2 \lambda +1} y^{3}-x^{-2 m} \left (9 a +2+9 b m \,x^{m -1}\right ) \left (a \,x^{1-m}+b \right )^{-\lambda -2} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
|
| 13 |
\begin{align*}
y^{\prime } x&=a \,x^{4} y^{3}+\left (b \,x^{2}-1\right ) y+c x \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 14 |
\begin{align*}
y^{\prime } x&=a y^{3}+3 a b \,x^{n} y^{2}-b n \,x^{n}-2 a \,b^{3} x^{3 n} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 15 |
\begin{align*}
y^{\prime } x&=3 x^{2 n +1} y^{3}+\left (b x -n \right ) y+c \,x^{1-n} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 16 |
\begin{align*}
y^{\prime } x&=a \,x^{n +2} y^{3}+\left (b \,x^{n}-1\right ) y+c \,x^{n -1} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 17 |
\begin{align*}
x^{2} y^{\prime }&=y^{3}-3 a^{2} x^{4} y+2 a^{3} x^{6}+2 a \,x^{3} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
|
| 18 |
\begin{align*}
y^{\prime }&=-\left (a x +b \,x^{m}\right ) y^{3}+y^{2} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
|
| 19 |
\begin{align*}
y^{\prime }&=\frac {y^{3}}{\sqrt {a \,x^{2}+b x +c}}+y^{2} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
|
| 21 |
\begin{align*}
y^{\prime }&=-y^{3}+a \,{\mathrm e}^{\lambda x} y^{2} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
|
| 22 |
\begin{align*}
y^{\prime }&=-y^{3}+3 a^{2} {\mathrm e}^{2 \lambda x} y-2 a^{3} {\mathrm e}^{3 \lambda x}+a \lambda \,{\mathrm e}^{\lambda x} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
|
| 23 |
\begin{align*}
y^{\prime }&=-\frac {{\mathrm e}^{2 \lambda x} y^{3}}{3 \lambda }+\frac {2 \lambda ^{2} {\mathrm e}^{-\lambda x}}{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 24 |
\begin{align*}
y^{\prime }&=a \,{\mathrm e}^{2 \lambda x} y^{3}+b \,{\mathrm e}^{\lambda x} y^{2}+c y+d \,{\mathrm e}^{-\lambda x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 25 |
\begin{align*}
y^{\prime }&=a \,{\mathrm e}^{\lambda x} y^{3}+3 a b \,{\mathrm e}^{\lambda x} y^{2}+c y-2 a \,b^{3} {\mathrm e}^{\lambda x}+b c \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 26 |
\begin{align*}
y^{\prime }&=a \,{\mathrm e}^{\lambda x} y^{3}+3 a b \,{\mathrm e}^{\left (\lambda +\mu \right ) x} y^{2}-2 a \,b^{3} {\mathrm e}^{\left (\lambda +3 \mu \right ) x}-{\mathrm e}^{\mu x} b \mu \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| ID | problem | ODE | Solved? | Maple | Mma | Sympy |
| 1 |
\begin{align*}
y^{\prime \prime }+a y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 2 |
\begin{align*}
y^{\prime \prime }-\left (a x +b \right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 3 |
\begin{align*}
y^{\prime \prime }-\left (a^{2} x^{2}+a \right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 4 |
\begin{align*}
y^{\prime \prime }-\left (a \,x^{2}+b \right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
|
| 5 |
\begin{align*}
y^{\prime \prime }+a^{3} x \left (-a x +2\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 6 |
\begin{align*}
y^{\prime \prime }-\left (a \,x^{2}+b x c \right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
|
| 7 |
\begin{align*}
y^{\prime \prime }-a \,x^{n} y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 8 |
\begin{align*}
y^{\prime \prime }-a \left (a \,x^{2 n}+n \,x^{n -1}\right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
|
| 9 |
\begin{align*}
y^{\prime \prime }-a \,x^{-2+n} \left (a \,x^{n}+n +1\right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
|
| 10 |
\begin{align*}
y^{\prime \prime }+\left (a \,x^{2 n}+b \,x^{n -1}\right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
|
| ID | problem | ODE | Solved? | Maple | Mma | Sympy |
| 11 |
\begin{align*}
b y+a y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 12 |
\begin{align*}
y^{\prime \prime }+a y^{\prime }+\left (b x +c \right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 13 |
\begin{align*}
y^{\prime \prime }+a y^{\prime }-\left (b \,x^{2}+c \right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
|
| 14 |
\begin{align*}
y^{\prime \prime }+a y^{\prime }+b \left (-b \,x^{2}+a x +1\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 15 |
\begin{align*}
y^{\prime \prime }+a y^{\prime }+b x \left (-b \,x^{3}+a x +2\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 16 |
\begin{align*}
y^{\prime \prime }+a y^{\prime }+b \left (-b \,x^{2 n}+a \,x^{n}+n \,x^{n -1}\right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
|
| 17 |
\begin{align*}
y^{\prime \prime }+a y^{\prime }+b \left (-b \,x^{2 n}-a \,x^{n}+n \,x^{n -1}\right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
|
| 18 |
\begin{align*}
y^{\prime \prime }+y^{\prime } x +\left (n -1\right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
|
| 19 |
\begin{align*}
2 n y-2 y^{\prime } x +y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
|
| 20 |
\begin{align*}
b y+a x y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
|
| 21 |
\begin{align*}
y^{\prime \prime }+a x y^{\prime }+b x y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
|
| 22 |
\begin{align*}
y^{\prime \prime }+a x y^{\prime }+\left (b x +c \right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
|
| 23 |
\begin{align*}
y^{\prime \prime }+2 a x y^{\prime }+\left (b \,x^{4}+a^{2} x^{2}+c x +a \right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
|
| 24 |
\begin{align*}
y^{\prime \prime }+\left (a x +b \right ) y^{\prime }-a y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 25 |
\begin{align*}
y^{\prime \prime }+\left (a x +b \right ) y^{\prime }+a y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 26 |
\begin{align*}
y^{\prime \prime }+\left (a x +b \right ) y^{\prime }+c \left (a x +b -c \right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 27 |
\begin{align*}
y^{\prime \prime }+\left (a x +2 b \right ) y^{\prime }+\left (a b x +b^{2}-a \right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 28 |
\begin{align*}
y^{\prime \prime }+\left (a x +b \right ) y^{\prime }+\left (c x +d \right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
|
| 29 |
\begin{align*}
y^{\prime \prime }+\left (a x +b \right ) y^{\prime }+c \left (\left (a -c \right ) x^{2}+b x +1\right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
|
| 30 |
\begin{align*}
y^{\prime \prime }+2 \left (a x +b \right ) y^{\prime }+\left (a^{2} x^{2}+2 a b x +c \right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 31 |
\begin{align*}
y^{\prime \prime }+\left (a x +b \right ) y^{\prime }+\left (\alpha \,x^{2}+\beta x +\gamma \right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
|
| 32 |
\begin{align*}
y^{\prime \prime }+\left (a x +b \right ) y^{\prime }+c \left (-c \,x^{2 n}+a \,x^{n +1}+b \,x^{n}+n \,x^{n -1}\right ) y&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
|
| 33 |
\begin{align*}
y^{\prime \prime }+a \left (-b^{2}+x^{2}\right ) y^{\prime }-a \left (x +b \right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 34 |
\begin{align*}
y^{\prime \prime }+\left (a \,x^{2}+b \right ) y^{\prime }+c \left (a \,x^{2}+b -c \right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 35 |
\begin{align*}
y^{\prime \prime }+\left (a \,x^{2}+2 b \right ) y^{\prime }+\left (b \,x^{2} a -a x +b^{2}\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 36 |
\begin{align*}
y^{\prime \prime }+\left (2 x^{2}+a \right ) y^{\prime }+\left (x^{4}+a \,x^{2}+b +2 x \right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 37 |
\begin{align*}
y^{\prime \prime }+\left (a \,x^{2}+b x \right ) y^{\prime }+\left (\alpha \,x^{2}+\beta x +\gamma \right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
|
| 38 |
\begin{align*}
y^{\prime \prime }+\left (b \,x^{2} a +b x +2 a \right ) y^{\prime }+a^{2} \left (b \,x^{2}+1\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 39 |
\begin{align*}
y^{\prime \prime }+\left (a \,x^{2}+b x +c \right ) y^{\prime }+x \left (b \,x^{2} a +b c +2 a \right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 40 |
\begin{align*}
y^{\prime \prime }+\left (a \,x^{2}+b x +c \right ) y^{\prime }+\left (a \,x^{3} b +a c \,x^{2}+b \right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 41 |
\begin{align*}
y^{\prime \prime }+\left (a \,x^{3}+2 b \right ) y^{\prime }+\left (a \,x^{3} b -a \,x^{2}+b^{2}\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 42 |
\begin{align*}
y^{\prime \prime }+\left (a \,x^{3}+b x \right ) y^{\prime }+2 \left (2 a \,x^{2}+b \right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 43 |
\begin{align*}
y^{\prime \prime }+\left (a \,x^{3} b +b \,x^{2}+2 a \right ) y^{\prime }+a^{2} \left (b \,x^{3}+1\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 44 |
\begin{align*}
y^{\prime \prime }+a \,x^{n} y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 45 |
\begin{align*}
y^{\prime \prime }+a \,x^{n} y^{\prime }+b \,x^{n -1} y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
|
| 46 |
\begin{align*}
y^{\prime \prime }+2 a \,x^{n} y^{\prime }+a \left (a \,x^{2 n}+n \,x^{n -1}\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 47 |
\begin{align*}
y^{\prime \prime }+a \,x^{n} y^{\prime }+\left (b \,x^{2 n}+c \,x^{n -1}\right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
|
| 48 |
\begin{align*}
y^{\prime \prime }+a \,x^{n} y^{\prime }-b \left (a \,x^{n +m}+b \,x^{2 m}+m \,x^{m -1}\right ) y&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
|
| 49 |
\begin{align*}
y^{\prime \prime }+2 a \,x^{n} y^{\prime }+\left (a^{2} x^{2 n}+b \,x^{2 m}+x^{n -1} a n +c \,x^{m -1}\right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
|
| 50 |
\begin{align*}
y^{\prime \prime }+\left (a \,x^{n}+b \right ) y^{\prime }+c \left (a \,x^{n}+b -c \right ) y&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
|
| 51 |
\begin{align*}
y^{\prime \prime }+\left (a \,x^{n}+2 b \right ) y^{\prime }+\left (a b \,x^{n}-a \,x^{n -1}+b^{2}\right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
|
| 52 |
\begin{align*}
y^{\prime \prime }+\left (a b \,x^{n}+b \,x^{n -1}+2 a \right ) y^{\prime }+a^{2} \left (b \,x^{n}+1\right ) y&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
|
| 53 |
\begin{align*}
y^{\prime \prime }+\left (a b \,x^{n}+2 b \,x^{n -1}-a^{2} x \right ) y^{\prime }+a \left (a b \,x^{n}+b \,x^{n -1}-a^{2} x \right ) y&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
|
| 54 |
\begin{align*}
y^{\prime \prime }+x^{n} \left (a \,x^{2}+\left (a c +b \right ) x +b c \right ) y^{\prime }-x^{n} \left (a x +b \right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
|
| 55 |
\begin{align*}
y^{\prime \prime }+\left (a \,x^{n}+b \,x^{m}\right ) y^{\prime }-\left (a \,x^{n -1}+b \,x^{m -1}\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 56 |
\begin{align*}
y^{\prime \prime }+\left (a \,x^{n}+b \,x^{m}\right ) y^{\prime }+\left (x^{n -1} a n +b m \,x^{m -1}\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 57 |
\begin{align*}
y^{\prime \prime }+\left (a \,x^{n}+b \,x^{m}\right ) y^{\prime }+\left (a \left (n +1\right ) x^{n -1}+b \left (m +1\right ) x^{m -1}\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
|
| 58 |
\begin{align*}
y^{\prime \prime }+\left (a \,x^{n}+b \,x^{m}\right ) y^{\prime }+c \left (a \,x^{n}+b \,x^{m}-c \right ) y&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
|
| 59 |
\begin{align*}
y^{\prime \prime }+\left (a \,x^{n}+b \,x^{m}\right ) y^{\prime }+\left (x^{n +m} a b +b \left (m +1\right ) x^{m -1}-a \,x^{n -1}\right ) y&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
|
| 60 |
\begin{align*}
y^{\prime \prime }+\left (a \,x^{n}+b \,x^{m}+c \right ) y^{\prime }+\left (x^{n +m} a b +x^{m} b c +x^{n -1} a n \right ) y&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
|
| ID | problem | ODE | Solved? | Maple | Mma | Sympy |
| 61 |
\begin{align*}
y^{\prime \prime } x +\frac {y^{\prime }}{2}+a y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 62 |
\begin{align*}
b y+a y^{\prime }+y^{\prime \prime } x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 63 |
\begin{align*}
b x y+a y^{\prime }+y^{\prime \prime } x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 64 |
\begin{align*}
y^{\prime \prime } x +a y^{\prime }+\left (b x +c \right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
|
| 65 |
\begin{align*}
y^{\prime \prime } x +n y^{\prime }+b \,x^{-2 n +1} y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 66 |
\begin{align*}
y^{\prime \prime } x +\left (1-3 n \right ) y^{\prime }-a^{2} n^{2} x^{2 n -1} y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
|
| 67 |
\begin{align*}
y^{\prime \prime } x +a y^{\prime }+b \,x^{n} y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 68 |
\begin{align*}
y^{\prime \prime } x +a y^{\prime }+b \,x^{n} \left (-b \,x^{n +1}+a +n \right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
|
| 69 |
\begin{align*}
y^{\prime \prime } x +a x y^{\prime }+a y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 70 |
\begin{align*}
y^{\prime \prime } x +\left (b -x \right ) y^{\prime }-a y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
|
| 71 |
\begin{align*}
y^{\prime \prime } x +\left (a x +b \right ) y^{\prime }+c \left (\left (a -c \right ) x +b \right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
|
| 72 |
\begin{align*}
y^{\prime \prime } x +\left (2 a x +b \right ) y^{\prime }+a \left (a x +b \right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 73 |
\begin{align*}
\left (a b x +a n +b m \right ) y+\left (m +n +\left (a +b \right ) x \right ) y^{\prime }+y^{\prime \prime } x&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
|
| 74 |
\begin{align*}
y^{\prime \prime } x +\left (a x +b \right ) y^{\prime }+\left (c x +d \right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
|
| 75 |
\begin{align*}
y^{\prime \prime } x -\left (a x +1\right ) y^{\prime }-b \,x^{2} \left (b x +a \right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 76 |
\begin{align*}
y^{\prime \prime } x -\left (2 a x +1\right ) y^{\prime }+\left (b \,x^{3}+a^{2} x +a \right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 77 |
\begin{align*}
y^{\prime \prime } x +\left (a x +b \right ) y^{\prime }+c x \left (-c \,x^{2}+a x +b +1\right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 78 |
\begin{align*}
y^{\prime \prime } x -\left (2 a x +1\right ) y^{\prime }+b \,x^{3} y&=0 \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
|
| 79 |
\begin{align*}
y^{\prime \prime } x +\left (b \,x^{2} a +b -5\right ) y^{\prime }+2 a^{2} \left (b -2\right ) x^{3} y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
|
| 80 |
\begin{align*}
y^{\prime \prime } x +\left (a \,x^{2}+b x \right ) y^{\prime }-\left (a c \,x^{2}+\left (b c +c^{2}+a \right ) x +b +2 c \right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 81 |
\begin{align*}
y^{\prime \prime } x +\left (a \,x^{2}+b x +2\right ) y^{\prime }+b y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 82 |
\begin{align*}
y^{\prime \prime } x +\left (a \,x^{2}+b x +c \right ) y^{\prime }+\left (2 a x +b \right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 83 |
\begin{align*}
y^{\prime \prime } x +\left (a \,x^{2}+b x +c \right ) y^{\prime }+\left (c -1\right ) \left (a x +b \right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 84 |
\begin{align*}
y^{\prime \prime } x +\left (a \,x^{2}+b x +c \right ) y^{\prime }+\left (A \,x^{2}+B x +\operatorname {C0} \right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
|
| 85 |
\begin{align*}
y^{\prime \prime } x +\left (a \,x^{2}+b x +2\right ) y^{\prime }+\left (c \,x^{2}+d x +b \right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
|
| 86 |
\begin{align*}
y^{\prime \prime } x +\left (a \,x^{3}+b \right ) y^{\prime }+a \left (b -1\right ) x^{2} y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 87 |
\begin{align*}
y^{\prime \prime } x +\left (a \,x^{2}+b \right ) x y^{\prime }+\left (3 a \,x^{2}+b \right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 88 |
\begin{align*}
y^{\prime \prime } x +\left (a \,x^{3}+b \,x^{2}+2\right ) y^{\prime }+b x y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 89 |
\begin{align*}
y^{\prime \prime } x +\left (a \,x^{3} b +b \,x^{2}+a x -1\right ) y^{\prime }+a^{2} b \,x^{3} y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 90 |
\begin{align*}
y^{\prime \prime } x +\left (a \,x^{3}+b \,x^{2}+c x +d \right ) y^{\prime }+\left (d -1\right ) \left (a \,x^{2}+b x +c \right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 91 |
\begin{align*}
y^{\prime \prime } x +a \,x^{n} y^{\prime }+\left (a b \,x^{n}-a \,x^{n -1}-b^{2} x +2 b \right ) y&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
|
| 92 |
\begin{align*}
y^{\prime \prime } x +\left (a \,x^{n}+2\right ) y^{\prime }+a \,x^{n -1} y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 93 |
\begin{align*}
y^{\prime \prime } x +\left (x^{n}+1-n \right ) y^{\prime }+b \,x^{2 n -1} y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
|
| 94 |
\begin{align*}
y^{\prime \prime } x +\left (a \,x^{n}+b \right ) y^{\prime }+x^{n -1} a n y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 95 |
\begin{align*}
y^{\prime \prime } x +\left (a \,x^{n}+b \right ) y^{\prime }+a \left (b -1\right ) x^{n -1} y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 96 |
\begin{align*}
y^{\prime \prime } x +\left (a \,x^{n}+b \right ) y^{\prime }+a \left (b +n -1\right ) x^{n -1} y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 97 |
\begin{align*}
y^{\prime \prime } x +\left (a \,x^{n}+b \right ) y^{\prime }+c \left (a \,x^{n}-c x +b \right ) y&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
|
| 98 |
\begin{align*}
y^{\prime \prime } x +\left (a b \,x^{n}+b -3 n +1\right ) y^{\prime }+a^{2} n \left (b -n \right ) x^{2 n -1} y&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
|
| 99 |
\begin{align*}
y^{\prime \prime } x +\left (a \,x^{n}+b \right ) y^{\prime }+\left (c \,x^{2 n -1}+d \,x^{n -1}\right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
|
| 100 |
\begin{align*}
y^{\prime \prime } x +\left (a \,x^{n}+b \,x^{n -1}+2\right ) y^{\prime }+b \,x^{-2+n} y&=0 \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
|
| 101 |
\begin{align*}
y^{\prime \prime } x +\left (a \,x^{n}+b x \right ) y^{\prime }+\left (a b \,x^{n}+x^{n -1} a n -b \right ) y&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
|
| 102 |
\begin{align*}
y^{\prime \prime } x +\left (a b \,x^{n}+b \,x^{n -1}+a x -1\right ) y^{\prime }+a^{2} b \,x^{n} y&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
|
| 103 |
\begin{align*}
y^{\prime \prime } x +\left (a \,x^{n}+b \,x^{m}+c \right ) y^{\prime }+\left (c -1\right ) \left (a \,x^{n -1}+b \,x^{m -1}\right ) y&=0 \\
\end{align*} |
✓ |
✗ |
✗ |
✗ |
|
| 104 |
\begin{align*}
y^{\prime \prime } x +\left (x^{n +m} a b +a n \,x^{n}+b \,x^{m}+1-2 n \right ) y^{\prime }+a^{2} b n \,x^{2 n +m -1} y&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
|
| 105 |
\begin{align*}
\left (a +x \right ) y^{\prime \prime }+\left (b x +c \right ) y^{\prime }+b y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 106 |
\begin{align*}
\left (a_{1} x +a_{0} \right ) y^{\prime \prime }+\left (b_{1} x +b_{0} \right ) y^{\prime }-m b_{1} y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
|
| 107 |
\begin{align*}
\left (a x +b \right ) y^{\prime \prime }+s \left (c x +d \right ) y^{\prime }-s^{2} \left (\left (a +c \right ) x +b +d \right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
|
| 108 |
\begin{align*}
\left (a_{2} x +b_{2} \right ) y^{\prime \prime }+\left (a_{1} x +b_{1} \right ) y^{\prime }+\left (a_{0} x +b_{0} \right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
|
| 109 |
\begin{align*}
\left (x +\gamma \right ) y^{\prime \prime }+\left (a \,x^{n}+b \,x^{m}+c \right ) y^{\prime }+\left (x^{n -1} a n +b m \,x^{m -1}\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
|
| ID | problem | ODE | Solved? | Maple | Mma | Sympy |
| 110 |
\begin{align*}
a y+x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 111 |
\begin{align*}
x^{2} y^{\prime \prime }+\left (a x +b \right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 112 |
\begin{align*}
x^{2} y^{\prime \prime }+\left (a^{2} x^{2}-n \left (n +1\right )\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 113 |
\begin{align*}
-\left (n \left (n +1\right )+a^{2} x^{2}\right ) y+x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 114 |
\begin{align*}
x^{2} y^{\prime \prime }-\left (a^{2} x^{2}+2 a b x +b^{2}-b \right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
|
| 115 |
\begin{align*}
x^{2} y^{\prime \prime }+\left (a \,x^{2}+b x +c \right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
|
| 116 |
\begin{align*}
x^{2} y^{\prime \prime }-\left (a \,x^{3}+\frac {5}{16}\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 117 |
\begin{align*}
x^{2} y^{\prime \prime }-\left (a^{2} x^{4}+a \left (2 b -1\right ) x^{2}+b \left (b +1\right )\right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
|
| 118 |
\begin{align*}
x^{2} y^{\prime \prime }+\left (a \,x^{n}+b \right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 119 |
\begin{align*}
x^{2} y^{\prime \prime }-\left (a^{2} x^{2 n}+a \left (2 b +n -1\right ) x^{n}+b \left (b -1\right )\right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
|
| 120 |
\begin{align*}
x^{2} y^{\prime \prime }+\left (a \,x^{2 n}+b \,x^{n}+c \right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
|
| 121 |
\begin{align*}
x^{2} y^{\prime \prime }+\left (a \,x^{3 n}+b \,x^{2 n}+\frac {1}{4}-\frac {n^{2}}{4}\right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
|
| 122 |
\begin{align*}
x^{2} y^{\prime \prime }+\left (a \,x^{2 n} \left (b \,x^{n}+c \right )^{m}+\frac {1}{4}-\frac {n^{2}}{4}\right ) y&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
|
| 123 |
\begin{align*}
x^{2} y^{\prime \prime }+a x y^{\prime }+b y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 124 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\left (n +\frac {1}{2}\right )^{2}\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 125 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x -\left (x^{2}+\left (n +\frac {1}{2}\right )^{2}\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 126 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (-\nu ^{2}+x^{2}\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 127 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x -\left (\nu ^{2}+x^{2}\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 128 |
\begin{align*}
x^{2} y^{\prime \prime }+2 y^{\prime } x -\left (a^{2} x^{2}+2\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 129 |
\begin{align*}
\left (a \left (1+a \right )+b^{2} x^{2}\right ) y-2 a x y^{\prime }+x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 130 |
\begin{align*}
x^{2} y^{\prime \prime }-2 a x y^{\prime }+\left (-b^{2} x^{2}+a \left (1+a \right )\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 131 |
\begin{align*}
x^{2} y^{\prime \prime }+\lambda x y^{\prime }+\left (a \,x^{2}+b x +c \right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
|
| 132 |
\begin{align*}
x^{2} y^{\prime \prime }+a x y^{\prime }+\left (b \,x^{n}+c \right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 133 |
\begin{align*}
x^{2} y^{\prime \prime }+a x y^{\prime }+x^{n} \left (b \,x^{n}+c \right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
|
| 134 |
\begin{align*}
x^{2} y^{\prime \prime }+\left (a x +b \right ) y^{\prime }+c y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
|
| 135 |
\begin{align*}
x^{2} y^{\prime \prime }+a \,x^{2} y^{\prime }+\left (b \,x^{2}+c x +d \right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
|
| 136 |
\begin{align*}
x^{2} y^{\prime \prime }+\left (a \,x^{2}+b \right ) y^{\prime }+c \left (\left (a -c \right ) x^{2}+b \right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
|
| 137 |
\begin{align*}
x^{2} y^{\prime \prime }+\left (a \,x^{2}+b x \right ) y^{\prime }-b y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 138 |
\begin{align*}
x^{2} y^{\prime \prime }+\left (a \,x^{2}+b x \right ) y^{\prime }+\left (k \left (a -k \right ) x^{2}+\left (a n +b k -2 k n \right ) x +n \left (b -n -1\right )\right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
|
| 139 |
\begin{align*}
a_{2} x^{2} y^{\prime \prime }+\left (a_{1} x^{2}+b_{1} x \right ) y^{\prime }+\left (a_{0} x^{2}+b_{0} x +c_{0} \right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
|
| 140 |
\begin{align*}
x^{2} y^{\prime \prime }+\left (a \,x^{2}+\left (a b -1\right ) x +b \right ) y^{\prime }+a^{2} b x y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 141 |
\begin{align*}
x^{2} y^{\prime \prime }-2 x \left (x^{2}-a \right ) y^{\prime }+\left (2 n \,x^{2}+\left (\left (-1\right )^{n}-1\right ) a \right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
|
| 142 |
\begin{align*}
x^{2} y^{\prime \prime }+x \left (a \,x^{2}+b x +c \right ) y^{\prime }+\left (A \,x^{3}+B \,x^{2}+C x +d \right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
|
| 143 |
\begin{align*}
x^{2} y^{\prime \prime }+a \,x^{n} y^{\prime }-\left (a b \,x^{n}+a c \,x^{n -1}+b^{2} x^{2}+2 b x c +c^{2}-c \right ) y&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
|
| 144 |
\begin{align*}
x^{2} y^{\prime \prime }+a \,x^{n} y^{\prime }+\left (a b \,x^{n +2 m}-b^{2} x^{4 m +2}+a m \,x^{n -1}-m^{2}-m \right ) y&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
|
| 145 |
\begin{align*}
x^{2} y^{\prime \prime }+\left (a \,x^{n}+b \right ) y^{\prime } x +b \left (a \,x^{n}-1\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 146 |
\begin{align*}
x^{2} y^{\prime \prime }+\left (a \,x^{n}+b \right ) y^{\prime } x +\left (\alpha \,x^{2 n}+\beta \,x^{n}+\gamma \right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
|
| 147 |
\begin{align*}
x^{2} y^{\prime \prime }+x \left (2 a \,x^{n}+b \right ) y^{\prime }+\left (a^{2} x^{2 n}+a \left (b +n -1\right ) x^{n}+\alpha \,x^{2 m}+\beta \,x^{m}+\gamma \right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
|
| 148 |
\begin{align*}
x^{2} y^{\prime \prime }+\left (a \,x^{n +2}+b \,x^{2}+c \right ) y^{\prime }+\left (a n \,x^{n +1}+x^{n} a c +b c \right ) y&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
|
| ID | problem | ODE | Solved? | Maple | Mma | Sympy |
| 149 |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }+n \left (n -1\right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
|
| 150 |
\begin{align*}
\left (-a^{2}+x^{2}\right ) y^{\prime \prime }+b y^{\prime }-6 y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
|
| 151 |
\begin{align*}
\left (x^{2}-1\right ) y^{\prime \prime }+y^{\prime } x +a y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 152 |
\begin{align*}
n^{2} y-y^{\prime } x +\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 153 |
\begin{align*}
n \left (n +1\right ) y-2 y^{\prime } x +\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
|
| 154 |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +\nu \left (\nu +1\right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
|
| 155 |
\begin{align*}
n \left (n +2\right ) y-3 y^{\prime } x +\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 156 |
\begin{align*}
\left (x^{2}-1\right ) y^{\prime \prime }+2 \left (n +1\right ) x y^{\prime }-\left (\nu +n +1\right ) \left (\nu -n \right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
|
| 157 |
\begin{align*}
\left (x^{2}-1\right ) y^{\prime \prime }-2 \left (n -1\right ) x y^{\prime }-\left (\nu -n +1\right ) \left (\nu +n \right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
|
| 158 |
\begin{align*}
\left (x^{2}-1\right ) y^{\prime \prime }+\left (2 a +1\right ) y^{\prime }-b \left (2 a +b \right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
|
| 159 |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }+\left (2 a -3\right ) x y^{\prime }+\left (n +1\right ) \left (n +2 a -1\right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
|
| 160 |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }+\left (\beta -\alpha -\left (\alpha +\beta +2\right ) x \right ) y^{\prime }+n \left (n +\alpha +\beta +1\right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
|
| 161 |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }+\left (\alpha -\beta +\left (\alpha +\beta -2\right ) x \right ) y^{\prime }+\left (n +1\right ) \left (n +\alpha +\beta \right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
|
| 162 |
\begin{align*}
\left (a \,x^{2}+b \right ) y^{\prime \prime }+a x y^{\prime }+c y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 163 |
\begin{align*}
\left (x^{2}+a \right ) y^{\prime \prime }+2 b x y^{\prime }+2 \left (b -1\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 164 |
\begin{align*}
\left (-a^{2}+x^{2}\right ) y^{\prime \prime }+2 b x y^{\prime }+b \left (b -1\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 165 |
\begin{align*}
\left (a^{2}+x^{2}\right ) y^{\prime \prime }+2 b x y^{\prime }+b \left (b -1\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 166 |
\begin{align*}
\left (a \,x^{2}+b \right ) y^{\prime \prime }+\left (2 n +1\right ) a x y^{\prime }+c y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
|
| 167 |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime } x +\left (2 a \,x^{2}+b \right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
|
| 168 |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }+\left (a x +b \right ) y^{\prime }+c y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
|
| 169 |
\begin{align*}
\left (a \,x^{2}+b \right ) y^{\prime \prime }+\left (c \,x^{2}+d \right ) y^{\prime }+\lambda \left (\left (-a \lambda +c \right ) x^{2}+d -b \lambda \right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
|
| 170 |
\begin{align*}
\left (a \,x^{2}+b \right ) y^{\prime \prime }+\left (\lambda \left (a +c \right ) x^{2}+\left (c -a \right ) x +2 b \lambda \right ) y^{\prime }+\lambda ^{2} \left (c \,x^{2}+b \right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
|
| 171 |
\begin{align*}
x \left (x -1\right ) y^{\prime \prime }+\left (\left (\alpha +\beta +1\right ) x -\gamma \right ) y^{\prime }+\alpha \beta y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
|
| 172 |
\begin{align*}
x \left (a +x \right ) y^{\prime \prime }+\left (b x +c \right ) y^{\prime }+d y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
|
| 173 |
\begin{align*}
2 x \left (x -1\right ) y^{\prime \prime }+\left (2 x -1\right ) y^{\prime }+\left (a x +b \right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
|
| 174 |
\begin{align*}
\left (2 a x +x^{2}+b \right ) y^{\prime \prime }+\left (a +x \right ) y^{\prime }-m^{2} y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 175 |
\begin{align*}
\left (a \,x^{2}+b x +c \right ) y^{\prime \prime }+\left (d x +k \right ) y^{\prime }+\left (d -2 a \right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 176 |
\begin{align*}
\left (a \,x^{2}+b x +c \right ) y^{\prime \prime }+\left (x k +d \right ) y^{\prime }-k y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 177 |
\begin{align*}
\left (a \,x^{2}+2 b x +c \right ) y^{\prime \prime }+\left (a x +b \right ) y^{\prime }+d y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 178 |
\begin{align*}
\left (a \,x^{2}+2 b x +c \right ) y^{\prime \prime }+3 \left (a x +b \right ) y^{\prime }+d y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 179 |
\begin{align*}
\left (a_{2} x^{2}+b_{2} x +c_{2} \right ) y^{\prime \prime }+\left (b_{1} x +c_{1} \right ) y^{\prime }+c_{0} y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
|
| 180 |
\begin{align*}
\left (a \,x^{2}+b x +c \right ) y^{\prime \prime }-\left (-k^{2}+x^{2}\right ) y^{\prime }+\left (k +x \right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
|
| 181 |
\begin{align*}
\left (a \,x^{2}+b x +c \right ) y^{\prime \prime }+\left (k^{3}+x^{3}\right ) y^{\prime }-\left (k^{2}-x k +x^{2}\right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
|
| ID | problem | ODE | Solved? | Maple | Mma | Sympy |
| 182 |
\begin{align*}
x^{3} y^{\prime \prime }+\left (a x +b \right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 183 |
\begin{align*}
x^{3} y^{\prime \prime }+\left (a \,x^{2}+b \right ) y^{\prime }+c x y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
|
| 184 |
\begin{align*}
x^{3} y^{\prime \prime }+\left (a \,x^{2}+b x \right ) y^{\prime }+b y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
|
| 185 |
\begin{align*}
x^{3} y^{\prime \prime }+\left (a \,x^{2}+b x \right ) y^{\prime }+c y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
|
| 186 |
\begin{align*}
x^{3} y^{\prime \prime }+\left (a \,x^{2}+b x \right ) y^{\prime }+\left (c x +d \right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
|
| 187 |
\begin{align*}
x^{3} y^{\prime \prime }+\left (a \,x^{3}+a b x -x^{2}+b \right ) y^{\prime }+a^{2} b x y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
|
| 188 |
\begin{align*}
x^{3} y^{\prime \prime }+\left (a \,x^{n}+b \right ) y^{\prime } x -\left (a \,x^{n}-a b \,x^{n -1}+b \right ) y&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
|
| 189 |
\begin{align*}
x \left (a \,x^{2}+b \right ) y^{\prime \prime }+2 \left (a \,x^{2}+b \right ) y^{\prime }-2 a x y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 190 |
\begin{align*}
x \left (x^{2}+a \right ) y^{\prime \prime }+\left (b \,x^{2}+c \right ) y^{\prime }+s x y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
|
| 191 |
\begin{align*}
x^{2} \left (a x +b \right ) y^{\prime \prime }+\left (c \,x^{2}+\left (a \lambda +2 b \right ) x +b \lambda \right ) y^{\prime }+\lambda \left (c -2 a \right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
|
| 192 |
\begin{align*}
x^{2} \left (a x +b \right ) y^{\prime \prime }-2 x \left (a x +2 b \right ) y^{\prime }+2 \left (a x +3 b \right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 193 |
\begin{align*}
x^{2} \left (a x +b \right ) y^{\prime \prime }+\left (a \left (2-n -m \right ) x^{2}-b \left (n +m \right ) x \right ) y^{\prime }+\left (a m \left (n -1\right ) x +b n \left (m +1\right )\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 194 |
\begin{align*}
x^{2} \left (x +a_{2} \right ) y^{\prime \prime }+x \left (b_{1} x +a_{1} \right ) y^{\prime }+\left (b_{0} x +a_{0} \right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
|
| 195 |
\begin{align*}
\left (a \,x^{3}+b \,x^{2}+c x \right ) y^{\prime \prime }+\left (\alpha \,x^{2}+\beta x +2 c \right ) y^{\prime }+\left (\beta -2 b \right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
|
| 196 |
\begin{align*}
\left (a \,x^{3}+b \,x^{2}+c x \right ) y^{\prime \prime }+\left (\alpha \,x^{2}+\beta x +2 c \right ) y^{\prime }-\left (x \alpha +2 b -\beta \right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
|
| 197 |
\begin{align*}
\left (a \,x^{3}+b \,x^{2}+c x \right ) y^{\prime \prime }+\left (-2 a \,x^{2}-\left (b +1\right ) x +k \right ) y^{\prime }+2 \left (a x +1\right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
|
| 198 |
\begin{align*}
\left (a \,x^{3}+b \,x^{2}+c x \right ) y^{\prime \prime }+\left (n \,x^{2}+x m +k \right ) y^{\prime }+\left (-1+k \right ) \left (\left (-a k +n \right ) x +m -b k \right ) y&=0 \\
\end{align*} |
✗ |
✗ |
✓ |
✗ |
|
| 200 |
\begin{align*}
\left (a \,x^{3}+b \,x^{2}+c x \right ) y^{\prime \prime }+\left (n \,x^{2}+x m +k \right ) y^{\prime }+\left (-2 \left (a +n \right ) x +1\right ) y&=0 \\
\end{align*} |
✗ |
✗ |
✓ |
✗ |
|
| 201 |
\begin{align*}
\left (a \,x^{3}+x^{2}+b \right ) y^{\prime \prime }+a^{2} x \left (x^{2}-b \right ) y^{\prime }-a^{3} b x y&=0 \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
|
| 202 |
\begin{align*}
2 x \left (a \,x^{2}+b x +c \right ) y^{\prime \prime }+\left (a \,x^{2}-c \right ) y^{\prime }+\lambda \,x^{2} y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 203 |
\begin{align*}
x \left (a \,x^{2}+b x +1\right ) y^{\prime \prime }+\left (\alpha \,x^{2}+\beta x +\gamma \right ) y^{\prime }+\left (x n +m \right ) y&=0 \\
\end{align*} |
✗ |
✗ |
✓ |
✗ |
|
| 204 |
\begin{align*}
x \left (x -1\right ) \left (x -a \right ) y^{\prime \prime }+\left (\left (\alpha +\beta +1\right ) x^{2}-\left (\alpha +\beta +1+a \left (\gamma +d \right )-a \right ) x +a \gamma \right ) y^{\prime }+\left (\alpha \beta x -q \right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
|
| 205 |
\begin{align*}
\left (a \,x^{3}+b \,x^{2}+c x +d \right ) y^{\prime \prime }-\left (-\lambda ^{2}+x^{2}\right ) y^{\prime }+\left (x +\lambda \right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
|
| 206 |
\begin{align*}
2 \left (a \,x^{3}+b \,x^{2}+c x +d \right ) y^{\prime \prime }+\left (3 a \,x^{2}+2 b x +c \right ) y^{\prime }+\lambda y&=0 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
|
| 207 |
\begin{align*}
2 \left (a \,x^{3}+b \,x^{2}+c x +d \right ) y^{\prime \prime }+3 \left (3 a \,x^{2}+2 b x +c \right ) y^{\prime }+\left (6 a x +2 b +\lambda \right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
|
| 208 |
\begin{align*}
\left (a \,x^{3}+b \,x^{2}+c x +d \right ) y^{\prime \prime }+\left (\alpha \,x^{2}+\left (\alpha \gamma +\beta \right ) x +\beta \lambda \right ) y^{\prime }-\left (x \alpha +\beta \right ) y&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
|
| 209 |
\begin{align*}
\left (a \,x^{3}+b \,x^{2}+c x +d \right ) y^{\prime \prime }+\left (\lambda ^{3}+x^{3}\right ) y^{\prime }-\left (\lambda ^{2}-\lambda x +x^{2}\right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
|
| 210 |
\begin{align*}
2 x \left (a \,x^{2}+b x +c \right ) y^{\prime \prime }+\left (a \left (2-k \right ) x^{2}+b \left (1-k \right ) x -c k \right ) y^{\prime }+\lambda \,x^{1+k} y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| ID | problem | ODE | Solved? | Maple | Mma | Sympy |
| 211 |
\begin{align*}
x^{4} y^{\prime \prime }+a y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 212 |
\begin{align*}
x^{4} y^{\prime \prime }+\left (a \,x^{2}+b x +c \right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
|
| 213 |
\begin{align*}
x^{4} y^{\prime \prime }-\left (a +b \right ) x^{2} y^{\prime }+\left (\left (a +b \right ) x +a b \right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 214 |
\begin{align*}
b y+2 x^{2} \left (a +x \right ) y^{\prime }+x^{4} y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 215 |
\begin{align*}
x^{4} y^{\prime \prime }+a \,x^{n} y^{\prime }-\left (a \,x^{n -1}+a b \,x^{-2+n}+b^{2}\right ) y&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
|
| 216 |
\begin{align*}
x^{2} \left (x -a \right )^{2} y^{\prime \prime }+b y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 217 |
\begin{align*}
x^{2} \left (x -a \right )^{2} y^{\prime \prime }+b y&=c \,x^{2} \left (x -a \right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 218 |
\begin{align*}
a \,x^{2} \left (x -1\right )^{2} y^{\prime \prime }+\left (b \,x^{2}+c x +d \right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
|
| 219 |
\begin{align*}
x^{2} \left (x^{2}+a \right ) y^{\prime \prime }+\left (b \,x^{2}+c \right ) x y^{\prime }+d y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
|
| 220 |
\begin{align*}
\left (x^{2}+1\right )^{2} y^{\prime \prime }+a y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 221 |
\begin{align*}
\left (x^{2}-1\right )^{2} y^{\prime \prime }+a y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 222 A |
\begin{align*}
\left (a^{2}+x^{2}\right )^{2} y^{\prime \prime }+b^{2} y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 222 B |
\begin{align*}
\left (-a^{2}+x^{2}\right )^{2} y^{\prime \prime }+b^{2} y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 223 |
\begin{align*}
4 \left (x^{2}+1\right )^{2} y^{\prime \prime }+\left (a \,x^{2}+a -3\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 224 |
\begin{align*}
\left (a \,x^{2}+b \right )^{2} y^{\prime \prime }+2 a x \left (a \,x^{2}+b \right ) y^{\prime }+c y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 225 |
\begin{align*}
\left (x^{2}-1\right )^{2} y^{\prime \prime }+2 x \left (x^{2}-1\right ) y^{\prime }-\left (\nu \left (\nu +1\right ) \left (x^{2}-1\right )+n^{2}\right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
|
| 226 |
\begin{align*}
\left (-x^{2}+1\right )^{2} y^{\prime \prime }-2 x \left (-x^{2}+1\right ) y^{\prime }+\left (\nu \left (\nu +1\right ) \left (-x^{2}+1\right )-\mu ^{2}\right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
|
| 227 |
\begin{align*}
a \left (x^{2}-1\right )^{2} y^{\prime \prime }+b x \left (x^{2}-1\right ) y^{\prime }+\left (c \,x^{2}+d x +e \right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
|
| 228 |
\begin{align*}
\left (a \,x^{2}+b \right )^{2} y^{\prime \prime }+\left (2 a x +c \right ) \left (a \,x^{2}+b \right ) y^{\prime }+k y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 229 |
\begin{align*}
\left (a \,x^{2}+b \right )^{2} y^{\prime \prime }+\left (a \,x^{2}+b \right ) \left (c \,x^{2}+d \right ) y^{\prime }+2 \left (-a d +b c \right ) x y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 230 |
\begin{align*}
\left (x^{2}+a \right )^{2} y^{\prime \prime }+b \,x^{n} \left (x^{2}+a \right ) y^{\prime }-\left (b \,x^{n +1}+a \right ) y&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
|
| 231 |
\begin{align*}
\left (x^{2}+a \right )^{2} y^{\prime \prime }+b \,x^{n} \left (x^{2}+a \right ) y^{\prime }-m \left (b \,x^{n +1}+\left (m -1\right ) x^{2}+a \right ) y&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
|
| 232 |
\begin{align*}
\left (x -a \right )^{2} \left (x -b \right )^{2} y^{\prime \prime }-c y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 233 |
\begin{align*}
\left (x -a \right )^{2} \left (x -b \right )^{2} y^{\prime \prime }+\left (x -a \right ) \left (x -b \right ) \left (2 x +\lambda \right ) y^{\prime }+\mu y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 234 |
\begin{align*}
\left (a \,x^{2}+b x +c \right )^{2} y^{\prime \prime }+A y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 235 |
\begin{align*}
\left (x^{2}-1\right )^{2} y^{\prime \prime }+2 x \left (x^{2}-1\right ) y^{\prime }+\left (\left (x^{2}-1\right ) \left (a^{2} x^{2}-\lambda \right )-m^{2}\right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
|
| 236 |
\begin{align*}
\left (x^{2}+1\right )^{2} y^{\prime \prime }+2 x \left (x^{2}+1\right ) y^{\prime }+\left (\left (x^{2}+1\right ) \left (a^{2} x^{2}-\lambda \right )+m^{2}\right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
|
| 237 |
\begin{align*}
\left (a \,x^{2}+b x +c \right )^{2} y^{\prime \prime }+\left (2 a x +k \right ) \left (a \,x^{2}+b x +c \right ) y^{\prime }+m y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| ID | problem | ODE | Solved? | Maple | Mma | Sympy |
| 238 |
\begin{align*}
a y-x^{5} y^{\prime }+x^{6} y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 239 |
\begin{align*}
x^{6} y^{\prime \prime }+x^{3} \left (3 x^{2}+a \right ) y^{\prime }+b y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 241 |
\begin{align*}
x^{n} y^{\prime \prime }+c \left (a x +b \right )^{n -4} y&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
|
| 242 |
\begin{align*}
x^{n} y^{\prime \prime }+a x y^{\prime }-\left (b^{2} x^{n}+2 b \,x^{n -1}+a b x +a \right ) y&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
|
| 243 |
\begin{align*}
x^{n} y^{\prime \prime }+\left (a x +b \right ) y^{\prime }-a y&=0 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
|
| 244 |
\begin{align*}
x^{n} y^{\prime \prime }+\left (a \,x^{n -1}+b x \right ) y^{\prime }+\left (-1+a \right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
|
| 245 |
\begin{align*}
x^{n} y^{\prime \prime }+\left (2 x^{n -1}+a \,x^{2}+b x \right ) y^{\prime }+b y&=0 \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
|
| 246 |
\begin{align*}
x^{n} y^{\prime \prime }+\left (a \,x^{n}+b \right ) y^{\prime }+c \left (\left (a -c \right ) x^{n}+b \right ) y&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
|
| 247 |
\begin{align*}
x^{n} y^{\prime \prime }+\left (a \,x^{n}-x^{n -1}+a b x +b \right ) y^{\prime }+a^{2} b x y&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
|
| 248 |
\begin{align*}
x^{n} y^{\prime \prime }+\left (a \,x^{n +m}+1\right ) y^{\prime }+a \,x^{m} \left (1+m \,x^{n -1}\right ) y&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
|
| 249 |
\begin{align*}
\left (a \,x^{n}+b \right ) y^{\prime \prime }+\left (c \,x^{n}+d \right ) y^{\prime }+\lambda \left (\left (-a \lambda +c \right ) x^{n}+d -b \lambda \right ) y&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
|
| 250 |
\begin{align*}
\left (a \,x^{n}+b x +c \right ) y^{\prime \prime }&=a n \left (n -1\right ) x^{-2+n} y \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
|
| 251 |
\begin{align*}
x \left (x^{n}+1\right ) y^{\prime \prime }+\left (\left (a -b \right ) x^{n}+a -n \right ) y^{\prime }+b \left (1-a \right ) x^{n -1} y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
|
| 252 |
\begin{align*}
x \left (x^{2 n}+a \right ) y^{\prime \prime }+\left (x^{2 n}+a -a n \right ) y^{\prime }-b^{2} x^{2 n -1} y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
|
| 253 |
\begin{align*}
x^{2} \left (a^{2} x^{2 n}-1\right ) y^{\prime \prime }+x \left (a^{2} \left (n +1\right ) x^{2 n}+n -1\right ) y^{\prime }-\nu \left (\nu +1\right ) a^{2} n^{2} x^{2 n} y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
|
| 254 |
\begin{align*}
x^{2} \left (a^{2} x^{2 n}-1\right ) y^{\prime \prime }+x \left (a p \,x^{n}+q \right ) y^{\prime }+\left (a r \,x^{n}+s \right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
|
| 255 |
\begin{align*}
\left (x^{n}+a \right )^{2} y^{\prime \prime }-b \,x^{-2+n} \left (\left (b -1\right ) x^{n}+a \left (n -1\right )\right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
|
| 256 |
\begin{align*}
\left (a \,x^{n}+b \right )^{2} y^{\prime \prime }+\left (a \,x^{n}+b \right ) \left (c \,x^{n}+d \right ) y^{\prime }+n \left (-a d +b c \right ) x^{n -1} y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
|
| 257 |
\begin{align*}
\left (x^{n}+a \right )^{2} y^{\prime \prime }+b \,x^{m} \left (x^{n}+a \right ) y^{\prime }-x^{-2+n} \left (b \,x^{m +1}+a n -a \right ) y&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
|
| 258 |
\begin{align*}
\left (a \,x^{n}+b \right )^{2} y^{\prime \prime }+c \,x^{m} \left (a \,x^{n}+b \right ) y^{\prime }+\left (c \,x^{m}-x^{n -1} a n -1\right ) y&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
|
| 259 |
\begin{align*}
x^{2} \left (a \,x^{n}+b \right )^{2} y^{\prime \prime }+\left (n +1\right ) x \left (a^{2} x^{2 n}-b^{2}\right ) y^{\prime }+c y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
|
| 260 |
\begin{align*}
\left (a \,x^{n +1}+b \,x^{n}+c \right )^{2} y^{\prime \prime }+\left (\alpha \,x^{n}+\beta \,x^{n -1}+\gamma \right ) y^{\prime }+\left (n \left (-a n -a +\alpha \right ) x^{n -1}+\left (n -1\right ) \left (-b n +\beta \right ) x^{-2+n}\right ) y&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
|
| 261 |
\begin{align*}
\left (a \,x^{n}+b \,x^{m}+c \right ) y^{\prime \prime }+\left (\lambda -x \right ) y^{\prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
|
| 262 |
\begin{align*}
\left (a \,x^{n}+b \,x^{m}+c \right ) y^{\prime \prime }+\left (\lambda ^{2}-x^{2}\right ) y^{\prime }+\left (x +\lambda \right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
|
| 263 |
\begin{align*}
2 \left (a \,x^{n}+b \,x^{m}+c \right ) y^{\prime \prime }+a n \,x^{n -1} b m \,x^{m -1} y^{\prime }+d y&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
|
| 264 |
\begin{align*}
\left (a \,x^{n}+b \right )^{m +1} y^{\prime \prime }+\left (a \,x^{n}+b \right ) y^{\prime }-a n m \,x^{n -1} y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| ID | problem | ODE | Solved? | Maple | Mma | Sympy |
| 1 |
\begin{align*}
y^{\prime \prime }+a \,{\mathrm e}^{\lambda x} y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 2 |
\begin{align*}
y^{\prime \prime }+\left (a \,{\mathrm e}^{x}-b \right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 3 |
\begin{align*}
y^{\prime \prime }+a \left (\lambda \,{\mathrm e}^{\lambda x}-a \,{\mathrm e}^{2 \lambda x}\right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
|
| 4 |
\begin{align*}
y^{\prime \prime }-\left (a^{2} {\mathrm e}^{2 x}+a \left (2 b +1\right ) {\mathrm e}^{x}+b^{2}\right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
|
| 5 |
\begin{align*}
y^{\prime \prime }-\left (a \,{\mathrm e}^{2 \lambda x}+b \,{\mathrm e}^{\lambda x}+c \right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
|
| 6 |
\begin{align*}
y^{\prime \prime }+\left (a \,{\mathrm e}^{4 \lambda x}+b \,{\mathrm e}^{3 \lambda x}+c \,{\mathrm e}^{2 \lambda x}-\frac {\lambda ^{2}}{4}\right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
|
| 7 |
\begin{align*}
y^{\prime \prime }+\left (a \,{\mathrm e}^{2 \lambda x} \left (b \,{\mathrm e}^{\lambda x}+c \right )^{n}-\frac {\lambda ^{2}}{4}\right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
|
| 8 |
\begin{align*}
b \,{\mathrm e}^{2 a x} y+a y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 9 |
\begin{align*}
y^{\prime \prime }-a y^{\prime }+b \,{\mathrm e}^{2 a x} y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 10 |
\begin{align*}
y^{\prime \prime }+a y^{\prime }+\left (b \,{\mathrm e}^{\lambda x}+c \right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 11 |
\begin{align*}
y^{\prime \prime }-y^{\prime }+\left (a \,{\mathrm e}^{3 \lambda x}+b \,{\mathrm e}^{2 \lambda x}+\frac {1}{4}-\frac {\lambda ^{2}}{4}\right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
|
| 12 |
\begin{align*}
y^{\prime \prime }-y^{\prime }+\left (a \,{\mathrm e}^{2 \lambda x} \left (b \,{\mathrm e}^{\lambda x}+c \right )^{n}+\frac {1}{4}-\frac {\lambda ^{2}}{4}\right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
|
| 13 |
\begin{align*}
y^{\prime \prime }+2 a \,{\mathrm e}^{\lambda x} y^{\prime }+a \,{\mathrm e}^{\lambda x} \left (a \,{\mathrm e}^{\lambda x}+\lambda \right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 14 |
\begin{align*}
y^{\prime \prime }+\left (a +b \right ) {\mathrm e}^{\lambda x} y^{\prime }+a \,{\mathrm e}^{\lambda x} \left (b \,{\mathrm e}^{\lambda x}+\lambda \right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
|
| 15 |
\begin{align*}
y^{\prime \prime }+a \,{\mathrm e}^{\lambda x} y^{\prime }-b \,{\mathrm e}^{\mu x} \left (a \,{\mathrm e}^{\lambda x}+b \,{\mathrm e}^{\mu x}+\mu \right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
|
| 16 |
\begin{align*}
y^{\prime \prime }+2 k \,{\mathrm e}^{\mu x} y^{\prime }+\left (a \,{\mathrm e}^{2 \lambda x}+b \,{\mathrm e}^{\lambda x}+k^{2} {\mathrm e}^{2 \mu x}+k \mu \,{\mathrm e}^{\mu x}+c \right ) y&=0 \\
\end{align*} |
✗ |
✗ |
✓ |
✗ |
|
| 17 |
\begin{align*}
y^{\prime \prime }-\left (a +2 b \,{\mathrm e}^{a x}\right ) y^{\prime }+b^{2} {\mathrm e}^{2 a x} y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 18 |
\begin{align*}
y^{\prime \prime }+\left (a \,{\mathrm e}^{2 \lambda x}+\lambda \right ) y^{\prime }-a \lambda \,{\mathrm e}^{2 \lambda x} y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
|
| 19 |
\begin{align*}
y^{\prime \prime }+\left (a \,{\mathrm e}^{\lambda x}-\lambda \right ) y^{\prime }+b \,{\mathrm e}^{2 \lambda x} y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 20 |
\begin{align*}
y^{\prime \prime }+\left (a \,{\mathrm e}^{\lambda x}+b \right ) y^{\prime }+c \left (a \,{\mathrm e}^{\lambda x}+b -c \right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
|
| 21 |
\begin{align*}
y^{\prime \prime }+\left (a +b \,{\mathrm e}^{2 \lambda x}\right ) y^{\prime }+\lambda \left (a -\lambda -b \,{\mathrm e}^{2 \lambda x}\right ) y&=0 \\
\end{align*} |
✗ |
✗ |
✓ |
✗ |
|
| 22 |
\begin{align*}
y^{\prime \prime }+\left (a +b \,{\mathrm e}^{\lambda x}+b -3 \lambda \right ) y^{\prime }+a^{2} \lambda \left (b -\lambda \right ) {\mathrm e}^{2 \lambda x} y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
|
| 23 |
\begin{align*}
y^{\prime \prime }+\left (2 a \,{\mathrm e}^{\lambda x}-\lambda \right ) y^{\prime }+\left (a^{2} {\mathrm e}^{2 \lambda x}+c \,{\mathrm e}^{\mu x}\right ) y&=0 \\
\end{align*} |
✗ |
✗ |
✓ |
✗ |
|
| 24 |
\begin{align*}
y^{\prime \prime }+\left (2 a \,{\mathrm e}^{\lambda x}+b \right ) y^{\prime }+\left (a^{2} {\mathrm e}^{2 \lambda x}+a \left (b +\lambda \right ) {\mathrm e}^{\lambda x}+c \right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 25 |
\begin{align*}
y^{\prime \prime }+\left (a \,{\mathrm e}^{\lambda x}+2 b -\lambda \right ) y^{\prime }+\left (c \,{\mathrm e}^{2 \lambda x}+a b \,{\mathrm e}^{\lambda x}+b^{2}-b \lambda \right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
|
| 26 |
\begin{align*}
y^{\prime \prime }+\left (a \,{\mathrm e}^{x}+b \right ) y^{\prime }+\left (c \left (a -c \right ) {\mathrm e}^{2 x}+\left (a k +b c -2 c k +c \right ) {\mathrm e}^{x}+k \left (b -k \right )\right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
|
| 27 |
\begin{align*}
y^{\prime \prime }+\left (a \,{\mathrm e}^{\lambda x}+b \right ) y^{\prime }+\left (\alpha \,{\mathrm e}^{2 \lambda x}+\beta \,{\mathrm e}^{\lambda x}+\gamma \right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
|
| 28 |
\begin{align*}
y^{\prime \prime }+\left (2 a \,{\mathrm e}^{\lambda x}-\lambda \right ) y^{\prime }+\left (a^{2} {\mathrm e}^{2 \lambda x}+b \,{\mathrm e}^{2 \mu x}+c \,{\mathrm e}^{\mu x}+k \right ) y&=0 \\
\end{align*} |
✗ |
✗ |
✓ |
✗ |
|
| 29 |
\begin{align*}
y^{\prime \prime }+\left (2 a \,{\mathrm e}^{\lambda x}+b -\lambda \right ) y^{\prime }+\left (a^{2} {\mathrm e}^{2 \lambda x}+a b \,{\mathrm e}^{\lambda x}+c \,{\mathrm e}^{2 \mu x}+d \,{\mathrm e}^{\mu x}+k \right ) y&=0 \\
\end{align*} |
✗ |
✗ |
✓ |
✗ |
|
| 30 |
\begin{align*}
y^{\prime \prime }+\left (a \,{\mathrm e}^{\lambda x}+b \,{\mathrm e}^{\mu x}\right ) y^{\prime }+a \,{\mathrm e}^{\lambda x} \left (b \,{\mathrm e}^{\mu x}+\lambda \right ) y&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
|
| 31 |
\begin{align*}
y^{\prime \prime }+{\mathrm e}^{\lambda x} \left (a \,{\mathrm e}^{2 \mu x}+b \right ) y^{\prime }+\mu \left ({\mathrm e}^{\lambda x} \left (b -a \,{\mathrm e}^{2 \mu x}\right )-\mu \right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
|
| 32 |
\begin{align*}
y^{\prime \prime }+\left (a \,{\mathrm e}^{\lambda x}+b \,{\mathrm e}^{\mu x}+c \right ) y^{\prime }+\left (a \lambda \,{\mathrm e}^{\lambda x}+{\mathrm e}^{\mu x} b \mu \right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 33 |
\begin{align*}
y^{\prime \prime }+\left (a \,{\mathrm e}^{\lambda x}+b \,{\mathrm e}^{\mu x}+c \right ) y^{\prime }+\left (a b \,{\mathrm e}^{\left (\lambda +\mu \right ) x}+{\mathrm e}^{\lambda x} a c +{\mathrm e}^{\mu x} b \mu \right ) y&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
|
| 34 |
\begin{align*}
y^{\prime \prime }+\left (a \,{\mathrm e}^{\lambda x}+2 b \,{\mathrm e}^{\mu x}-\lambda \right ) y^{\prime }+\left (a b \,{\mathrm e}^{\left (\lambda +\mu \right ) x}+c \,{\mathrm e}^{2 \lambda x}+{\mathrm e}^{2 \mu x} b^{2}+b \left (\mu -\lambda \right ) {\mathrm e}^{\mu x}\right ) y&=0 \\
\end{align*} |
✗ |
✗ |
✓ |
✗ |
|
| 35 |
\begin{align*}
y^{\prime \prime }+\left (a \,{\mathrm e}^{\left (\lambda +\mu \right ) x}+a \lambda \,{\mathrm e}^{\lambda x}+b \,{\mathrm e}^{\mu x}-2 \lambda \right ) y^{\prime }+a^{2} b \lambda \,{\mathrm e}^{\left (2 \lambda +\mu \right ) x} y&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
|
| 36 |
\begin{align*}
y^{\prime \prime }+a \,{\mathrm e}^{b \,x^{n}} y^{\prime }+c \left (a \,{\mathrm e}^{b \,x^{n}}-c \right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
|
| 37 |
\begin{align*}
\left (a \,{\mathrm e}^{\lambda x}+b \right ) y^{\prime \prime }-a \,\lambda ^{2} {\mathrm e}^{\lambda x} y&=0 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
|
| 38 |
\begin{align*}
\left (a^{2} {\mathrm e}^{2 \lambda x}+b \right ) y^{\prime \prime }-b \lambda y^{\prime }-a^{2} \lambda ^{2} k^{2} {\mathrm e}^{2 \lambda x} y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 39 |
\begin{align*}
2 \left (a \,{\mathrm e}^{\lambda x}+b \right ) y^{\prime \prime }+a \lambda \,{\mathrm e}^{\lambda x} y^{\prime }+c y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 40 |
\begin{align*}
\left (a \,{\mathrm e}^{\lambda x}+b \right ) y^{\prime \prime }+\left (c \,{\mathrm e}^{\lambda x}+d \right ) y^{\prime }+k \left (\left (-a k +c \right ) {\mathrm e}^{\lambda x}+d -b k \right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
|
| 41 |
\begin{align*}
\left (a \,{\mathrm e}^{\lambda x}+b \right ) y^{\prime \prime }+\left (c \,{\mathrm e}^{\lambda x}+d \right ) y^{\prime }+\left (n \,{\mathrm e}^{\lambda x}+m \right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
|