| ID | problem | ODE | Solved? | Maple | Mma | Sympy |
| Problem 7 |
\begin{align*}
y^{\prime \prime }-25 y&=0 \\
\end{align*} |
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| Problem 8 |
\begin{align*}
y^{\prime \prime }+4 y&=0 \\
\end{align*} |
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| Problem 9 |
\begin{align*}
y^{\prime \prime }+y^{\prime }-2 y&=0 \\
\end{align*} |
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| Problem 10 |
\begin{align*}
y^{\prime }&=-y^{2} \\
\end{align*} |
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| Problem 11 |
\begin{align*}
y^{\prime }&=\frac {y}{2 x} \\
\end{align*} |
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| Problem 12 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }+5 y&=0 \\
\end{align*} |
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| Problem 13 |
\begin{align*}
y^{\prime \prime }-9 y&=0 \\
\end{align*} |
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| Problem 14 |
\begin{align*}
x^{2} y^{\prime \prime }+5 x y^{\prime }+3 y&=0 \\
\end{align*} |
✓ |
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| Problem 15 |
\begin{align*}
x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y&=0 \\
\end{align*} |
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| Problem 16 |
\begin{align*}
x^{2} y^{\prime \prime }-3 x y^{\prime }+13 y&=0 \\
\end{align*} |
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| Problem 17 |
\begin{align*}
2 x^{2} y^{\prime \prime }-x y^{\prime }+y&=9 x^{2} \\
\end{align*} |
✓ |
✓ |
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| Problem 18 |
\begin{align*}
x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y&=x^{4} \sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
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| Problem 19 |
\begin{align*}
y^{\prime \prime }-\left (a +b \right ) y^{\prime }+a b y&=0 \\
\end{align*} |
✓ |
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| Problem 20 |
\begin{align*}
y^{\prime \prime }-2 a y^{\prime }+a^{2} y&=0 \\
\end{align*} |
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| Problem 21 |
\begin{align*}
y^{\prime \prime }-2 a y^{\prime }+\left (a^{2}+b^{2}\right ) y&=0 \\
\end{align*} |
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| Problem 22 |
\begin{align*}
y^{\prime \prime }-y^{\prime }-6 y&=0 \\
\end{align*} |
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| Problem 23 |
\begin{align*}
y^{\prime \prime }+6 y^{\prime }+9 y&=0 \\
\end{align*} |
✓ |
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| Problem 24 | \begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }-y&=0 \\
\end{align*} | ✓ | ✓ | ✓ | ✓ |
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| Problem 25 |
\begin{align*}
x^{2} y^{\prime \prime }+5 x y^{\prime }+4 y&=0 \\
\end{align*} |
✓ |
✓ |
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| Problem 28 |
\begin{align*}
y^{\prime }&=\frac {{\mathrm e}^{x}-\sin \left (y\right )}{x \cos \left (y\right )} \\
\end{align*} |
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| Problem 29 |
\begin{align*}
y^{\prime }&=\frac {1-y^{2}}{2 y x +2} \\
\end{align*} |
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| Problem 30 |
\begin{align*}
y^{\prime }&=\frac {\left (1-y \,{\mathrm e}^{y x}\right ) {\mathrm e}^{-y x}}{x} \\
y \left (1\right ) &= 0 \\
\end{align*} |
✓ |
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| Problem 31 |
\begin{align*}
y^{\prime }&=\frac {x^{2} \left (1-y^{2}\right )+y \,{\mathrm e}^{\frac {y}{x}}}{x \left ({\mathrm e}^{\frac {y}{x}}+2 x^{2} y\right )} \\
\end{align*} |
✓ |
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| Problem 32 |
\begin{align*}
y^{\prime }&=\frac {\cos \left (x \right )-2 x y^{2}}{2 x^{2} y} \\
y \left (\pi \right ) &= \frac {1}{\pi } \\
\end{align*} |
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| Problem 33 |
\begin{align*}
y^{\prime }&=\sin \left (x \right ) \\
\end{align*} |
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| Problem 34 |
\begin{align*}
y^{\prime }&=\frac {1}{x^{{2}/{3}}} \\
\end{align*} |
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| Problem 35 |
\begin{align*}
y^{\prime \prime }&=x \,{\mathrm e}^{x} \\
\end{align*} |
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| Problem 36 |
\begin{align*}
y^{\prime \prime }&=x^{n} \\
\end{align*} |
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| Problem 37 |
\begin{align*}
y^{\prime }&=x^{2} \ln \left (x \right ) \\
y \left (1\right ) &= 2 \\
\end{align*} |
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| Problem 38 |
\begin{align*}
y^{\prime \prime }&=\cos \left (x \right ) \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
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| Problem 39 |
\begin{align*}
y^{\prime \prime \prime }&=6 x \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -1 \\
y^{\prime \prime }\left (0\right ) &= -4 \\
\end{align*} |
✓ |
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| Problem 40 |
\begin{align*}
y^{\prime \prime }&=x \,{\mathrm e}^{x} \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= 4 \\
\end{align*} |
✓ |
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| Problem 45 |
\begin{align*}
y^{\prime \prime }+y^{\prime }-6 y&=0 \\
\end{align*} |
✓ |
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| Problem 46 |
\begin{align*}
x^{2} y^{\prime \prime }-x y^{\prime }-8 y&=0 \\
\end{align*} |
✓ |
✓ |
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| Problem 47 |
\begin{align*}
x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y&=x^{2} \ln \left (x \right ) \\
\end{align*} |
✓ |
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| ID | problem | ODE | Solved? | Maple | Mma | Sympy |
| Problem 1 |
\begin{align*}
y^{\prime }&=2 y x \\
\end{align*} |
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| Problem 2 |
\begin{align*}
y^{\prime }&=\frac {y^{2}}{x^{2}+1} \\
\end{align*} |
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| Problem 3 |
\begin{align*}
{\mathrm e}^{x +y} y^{\prime }-1&=0 \\
\end{align*} |
✓ |
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| Problem 4 |
\begin{align*}
y^{\prime }&=\frac {y}{x \ln \left (x \right )} \\
\end{align*} |
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| Problem 5 |
\begin{align*}
y-\left (x -1\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
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| Problem 6 |
\begin{align*}
y^{\prime }&=\frac {2 x \left (-1+y\right )}{x^{2}+3} \\
\end{align*} |
✓ |
✓ |
✓ |
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| Problem 7 |
\begin{align*}
-x y^{\prime }+y&=3-2 x^{2} y^{\prime } \\
\end{align*} |
✓ |
✓ |
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| Problem 8 |
\begin{align*}
y^{\prime }&=\frac {\cos \left (x -y\right )}{\sin \left (x \right ) \sin \left (y\right )}-1 \\
\end{align*} |
✓ |
✓ |
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| Problem 9 |
\begin{align*}
y^{\prime }&=\frac {x \left (y^{2}-1\right )}{2 \left (x -2\right ) \left (x -1\right )} \\
\end{align*} |
✓ |
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| Problem 10 |
\begin{align*}
y^{\prime }&=\frac {x^{2} y-32}{-x^{2}+16}+2 \\
\end{align*} |
✓ |
✓ |
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| Problem 11 |
\begin{align*}
\left (x -a \right ) \left (x -b \right ) y^{\prime }-y+c&=0 \\
\end{align*} |
✓ |
✓ |
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| Problem 12 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime }+y^{2}&=-1 \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
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| Problem 13 |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime }+y x&=a x \\
y \left (0\right ) &= 2 a \\
\end{align*} |
✓ |
✓ |
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| Problem 14 |
\begin{align*}
y^{\prime }&=1-\frac {\sin \left (x +y\right )}{\cos \left (x \right ) \sin \left (y\right )} \\
y \left (\frac {\pi }{4}\right ) &= \frac {\pi }{4} \\
\end{align*} |
✓ |
✓ |
✓ |
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| Problem 15 |
\begin{align*}
y^{\prime }&=y^{3} \sin \left (x \right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
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| Problem 16 |
\begin{align*}
y^{\prime }&=\frac {2 \sqrt {-1+y}}{3} \\
y \left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
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| Problem 17 |
\begin{align*}
m v^{\prime }&=m g -k v^{2} \\
v \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
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| ID | problem | ODE | Solved? | Maple | Mma | Sympy |
| Problem 1 |
\begin{align*}
y^{\prime }+y&=4 \,{\mathrm e}^{x} \\
\end{align*} |
✓ |
✓ |
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| Problem 2 |
\begin{align*}
y^{\prime }+\frac {2 y}{x}&=5 x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
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| Problem 3 |
\begin{align*}
x^{2} y^{\prime }-4 y x&=x^{7} \sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
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| Problem 4 |
\begin{align*}
y^{\prime }+2 y x&=2 x^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
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| Problem 5 |
\begin{align*}
y^{\prime }+\frac {2 x y}{-x^{2}+1}&=4 x \\
\end{align*} |
✓ |
✓ |
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| Problem 6 |
\begin{align*}
y^{\prime }+\frac {2 x y}{x^{2}+1}&=\frac {4}{\left (x^{2}+1\right )^{2}} \\
\end{align*} |
✓ |
✓ |
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| Problem 7 |
\begin{align*}
2 \cos \left (x \right )^{2} y^{\prime }+y \sin \left (2 x \right )&=4 \cos \left (x \right )^{4} \\
\end{align*} |
✓ |
✓ |
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| Problem 8 |
\begin{align*}
y^{\prime }+\frac {y}{x \ln \left (x \right )}&=9 x^{2} \\
\end{align*} |
✓ |
✓ |
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| Problem 9 |
\begin{align*}
y^{\prime }-y \tan \left (x \right )&=8 \sin \left (x \right )^{3} \\
\end{align*} |
✓ |
✓ |
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| Problem 10 |
\begin{align*}
x^{\prime } t +2 x&=4 \,{\mathrm e}^{t} \\
\end{align*} |
✓ |
✓ |
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| Problem 11 |
\begin{align*}
y^{\prime }&=\sin \left (x \right ) \left (y \sec \left (x \right )-2\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
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| Problem 12 |
\begin{align*}
1-y \sin \left (x \right )-\cos \left (x \right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
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| Problem 13 |
\begin{align*}
y^{\prime }-\frac {y}{x}&=2 x^{2} \ln \left (x \right ) \\
\end{align*} |
✓ |
✓ |
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| Problem 14 |
\begin{align*}
y^{\prime }+\alpha y&={\mathrm e}^{\beta x} \\
\end{align*} |
✓ |
✓ |
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| Problem 15 |
\begin{align*}
y^{\prime }+\frac {m y}{x}&=\ln \left (x \right ) \\
\end{align*} |
✓ |
✓ |
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| Problem 16 |
\begin{align*}
y^{\prime }+\frac {2 y}{x}&=4 x \\
y \left (1\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
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| Problem 17 |
\begin{align*}
\sin \left (x \right ) y^{\prime }-\cos \left (x \right ) y&=\sin \left (2 x \right ) \\
y \left (\frac {\pi }{2}\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
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| Problem 18 | \begin{align*}
x^{\prime }+\frac {2 x}{4-t}&=5 \\
x \left (0\right ) &= 4 \\
\end{align*} | ✓ | ✓ | ✓ | ✓ |
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| Problem 19 |
\begin{align*}
y-{\mathrm e}^{x}+y^{\prime }&=0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
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| Problem 20 |
\begin{align*}
y^{\prime }-2 y&=\left \{\begin {array}{cc} 1 & x \le 1 \\ 0 & 1<x \end {array}\right . \\
y \left (0\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
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| Problem 21 |
\begin{align*}
y^{\prime }-2 y&=\left \{\begin {array}{cc} 1-x & x <1 \\ 0 & 1\le x \end {array}\right . \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
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| Problem 22 |
\begin{align*}
y^{\prime \prime }+\frac {y^{\prime }}{x}&=9 x \\
\end{align*} |
✓ |
✓ |
✓ |
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| Problem 30 |
\begin{align*}
y^{\prime }+\frac {y}{x}&=\cos \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
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| Problem 31 |
\begin{align*}
y^{\prime }+y&={\mathrm e}^{-2 x} \\
\end{align*} |
✓ |
✓ |
✓ |
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| Problem 32 |
\begin{align*}
y^{\prime }+y \cot \left (x \right )&=2 \cos \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
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| Problem 33 |
\begin{align*}
x y^{\prime }-y&=x^{2} \ln \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
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| ID | problem | ODE | Solved? | Maple | Mma | Sympy |
| Problem 9 |
\begin{align*}
y^{\prime }&=\frac {x^{2}+y x +y^{2}}{x^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
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| Problem 10 |
\begin{align*}
\left (3 x -y\right ) y^{\prime }&=3 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
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| Problem 11 |
\begin{align*}
y^{\prime }&=\frac {\left (x +y\right )^{2}}{2 x^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
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| Problem 12 |
\begin{align*}
\sin \left (\frac {y}{x}\right ) \left (x y^{\prime }-y\right )&=x \cos \left (\frac {y}{x}\right ) \\
\end{align*} |
✓ |
✓ |
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| Problem 13 |
\begin{align*}
x y^{\prime }&=\sqrt {16 x^{2}-y^{2}}+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
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| Problem 14 |
\begin{align*}
x y^{\prime }-y&=\sqrt {9 x^{2}+y^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
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| Problem 15 |
\begin{align*}
y \left (x^{2}-y^{2}\right )-x \left (x^{2}-y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
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| Problem 16 |
\begin{align*}
x y^{\prime }+y \ln \left (x \right )&=\ln \left (y\right ) y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
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| Problem 17 |
\begin{align*}
y^{\prime }&=\frac {y^{2}+2 y x -2 x^{2}}{x^{2}-y x +y^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
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| Problem 18 |
\begin{align*}
2 x y y^{\prime }-2 y^{2}-x^{2} {\mathrm e}^{-\frac {y^{2}}{x^{2}}}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
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| Problem 19 |
\begin{align*}
x^{2} y^{\prime }&=y^{2}+3 y x +x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
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| Problem 20 |
\begin{align*}
y y^{\prime }&=\sqrt {x^{2}+y^{2}}-x \\
\end{align*} |
✓ |
✓ |
✓ |
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| Problem 21 |
\begin{align*}
2 x \left (2 x +y\right ) y^{\prime }&=y \left (4 x -y\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
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| Problem 22 |
\begin{align*}
x y^{\prime }&=\tan \left (\frac {y}{x}\right ) x +y \\
\end{align*} |
✓ |
✓ |
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| Problem 23 |
\begin{align*}
y^{\prime }&=\frac {x \sqrt {x^{2}+y^{2}}+y^{2}}{y x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
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| Problem 25 |
\begin{align*}
y^{\prime }&=\frac {-2 x +4 y}{x +y} \\
y \left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
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| Problem 26 |
\begin{align*}
y^{\prime }&=\frac {2 x -y}{x +4 y} \\
y \left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
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| Problem 27 | \begin{align*}
y^{\prime }&=\frac {y-\sqrt {x^{2}+y^{2}}}{x} \\
y \left (3\right ) &= 4 \\
\end{align*} | ✓ | ✓ | ✓ | ✗ |
|
| Problem 28 |
\begin{align*}
x y^{\prime }-y&=\sqrt {4 x^{2}-y^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
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| Problem 29(a) |
\begin{align*}
y^{\prime }&=\frac {x +a y}{a x -y} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
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| Problem 29(b) |
\begin{align*}
y^{\prime }&=\frac {x +\frac {y}{2}}{\frac {x}{2}-y} \\
y \left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
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| Problem 38 |
\begin{align*}
y^{\prime }-\frac {y}{x}&=\frac {4 x^{2} \cos \left (x \right )}{y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
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| Problem 39 |
\begin{align*}
y^{\prime }+\frac {y \tan \left (x \right )}{2}&=2 y^{3} \sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
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| Problem 40 |
\begin{align*}
y^{\prime }-\frac {3 y}{2 x}&=6 y^{{1}/{3}} x^{2} \ln \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
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| Problem 41 |
\begin{align*}
y^{\prime }+\frac {2 y}{x}&=6 \sqrt {x^{2}+1}\, \sqrt {y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
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| Problem 42 |
\begin{align*}
y^{\prime }+\frac {2 y}{x}&=6 y^{2} x^{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
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| Problem 43 |
\begin{align*}
2 x \left (y^{\prime }+x^{2} y^{3}\right )+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
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| Problem 44 |
\begin{align*}
\left (x -a \right ) \left (x -b \right ) \left (y^{\prime }-\sqrt {y}\right )&=2 \left (b -a \right ) y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
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| Problem 45 |
\begin{align*}
y^{\prime }+\frac {6 y}{x}&=\frac {3 y^{{2}/{3}} \cos \left (x \right )}{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
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| Problem 46 |
\begin{align*}
y^{\prime }+4 y x&=4 x^{3} \sqrt {y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 47 |
\begin{align*}
y^{\prime }-\frac {y}{2 x \ln \left (x \right )}&=2 x y^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
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| Problem 48 |
\begin{align*}
y^{\prime }-\frac {y}{\left (\pi -1\right ) x}&=\frac {3 x y^{\pi }}{1-\pi } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 49 |
\begin{align*}
2 y^{\prime }+y \cot \left (x \right )&=\frac {8 \cos \left (x \right )^{3}}{y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 50 |
\begin{align*}
\left (1-\sqrt {3}\right ) y^{\prime }+y \sec \left (x \right )&=y^{\sqrt {3}} \sec \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 51 |
\begin{align*}
y^{\prime }+\frac {2 x y}{x^{2}+1}&=x y^{2} \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 52 |
\begin{align*}
y^{\prime }+y \cot \left (x \right )&=y^{3} \sin \left (x \right )^{3} \\
y \left (\frac {\pi }{2}\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 54 | \begin{align*}
y^{\prime }&=\left (9 x -y\right )^{2} \\
y \left (0\right ) &= 0 \\
\end{align*} | ✓ | ✓ | ✓ | ✓ |
|
| Problem 55 |
\begin{align*}
y^{\prime }&=\left (4 x +y+2\right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 56 |
\begin{align*}
y^{\prime }&=\sin \left (3 x -3 y+1\right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 58 |
\begin{align*}
y^{\prime }&=\frac {y \left (\ln \left (y x \right )-1\right )}{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 59 |
\begin{align*}
y^{\prime }&=2 x \left (x +y\right )^{2}-1 \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 60 |
\begin{align*}
y^{\prime }&=\frac {x +2 y-1}{2 x -y+3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 61 |
\begin{align*}
y^{\prime }+p \left (x \right ) y+q \left (x \right ) y^{2}&=r \left (x \right ) \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
|
| Problem 62 |
\begin{align*}
y^{\prime }+\frac {2 y}{x}-y^{2}&=-\frac {2}{x^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 63 |
\begin{align*}
y^{\prime }+\frac {7 y}{x}-3 y^{2}&=\frac {3}{x^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 64 |
\begin{align*}
\frac {y^{\prime }}{y}+p \left (x \right ) \ln \left (y\right )&=q \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| Problem 65 |
\begin{align*}
\frac {y^{\prime }}{y}-\frac {2 \ln \left (y\right )}{x}&=\frac {1-2 \ln \left (x \right )}{x} \\
y \left (1\right ) &= {\mathrm e} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 67 |
\begin{align*}
\sec \left (y\right )^{2} y^{\prime }+\frac {\tan \left (y\right )}{2 \sqrt {x +1}}&=\frac {1}{2 \sqrt {x +1}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| ID | problem | ODE | Solved? | Maple | Mma | Sympy |
| Problem 1 |
\begin{align*}
y \,{\mathrm e}^{y x}+\left (2 y-x \,{\mathrm e}^{y x}\right ) y^{\prime }&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
|
| Problem 2 |
\begin{align*}
\cos \left (y x \right )-x y \sin \left (y x \right )-x^{2} \sin \left (y x \right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 3 |
\begin{align*}
y+3 x^{2}+x y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 4 |
\begin{align*}
2 x \,{\mathrm e}^{y}+\left (3 y^{2}+x^{2} {\mathrm e}^{y}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 5 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime }+2 y x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 6 |
\begin{align*}
y^{2}-2 x +2 x y y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 7 |
\begin{align*}
4 \,{\mathrm e}^{2 x}+2 y x -y^{2}+\left (x -y\right )^{2} y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| Problem 8 |
\begin{align*}
\frac {1}{x}-\frac {y}{x^{2}+y^{2}}+\frac {x y^{\prime }}{x^{2}+y^{2}}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 9 |
\begin{align*}
y \cos \left (y x \right )-\sin \left (x \right )+x \cos \left (y x \right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| Problem 10 |
\begin{align*}
2 y^{2} {\mathrm e}^{2 x}+3 x^{2}+2 y \,{\mathrm e}^{2 x} y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 11 |
\begin{align*}
y^{2}+\cos \left (x \right )+\left (2 y x +\sin \left (y\right )\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| Problem 12 |
\begin{align*}
\sin \left (y\right )+\cos \left (x \right ) y+\left (x \cos \left (y\right )+\sin \left (x \right )\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| ID | problem | ODE | Solved? | Maple | Mma | Sympy |
| Problem 23 |
\begin{align*}
y^{\prime \prime }-2 y^{\prime }-3 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 24 |
\begin{align*}
y^{\prime \prime }+7 y^{\prime }+10 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 25 |
\begin{align*}
y^{\prime \prime }-36 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 26 |
\begin{align*}
y^{\prime \prime }+4 y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 27 |
\begin{align*}
y^{\prime \prime \prime }-3 y^{\prime \prime }-y^{\prime }+3 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 28 |
\begin{align*}
y^{\prime \prime \prime }+3 y^{\prime \prime }-4 y^{\prime }-12 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 29 |
\begin{align*}
y^{\prime \prime \prime }+3 y^{\prime \prime }-18 y^{\prime }-40 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 30 |
\begin{align*}
y^{\prime \prime \prime }-y^{\prime \prime }-2 y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 31 |
\begin{align*}
y^{\prime \prime \prime }+y^{\prime \prime }-10 y^{\prime }+8 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 32 |
\begin{align*}
y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }-y^{\prime \prime }+2 y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 33 |
\begin{align*}
y^{\prime \prime \prime \prime }-13 y^{\prime \prime }+36 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 34 |
\begin{align*}
x^{2} y^{\prime \prime }+3 x y^{\prime }-8 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 35 |
\begin{align*}
2 x^{2} y^{\prime \prime }+5 x y^{\prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 36 |
\begin{align*}
x^{3} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 37 |
\begin{align*}
x^{3} y^{\prime \prime \prime }+3 x^{2} y^{\prime \prime }-6 x y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 38 |
\begin{align*}
y^{\prime \prime }+y^{\prime }-6 y&=18 \,{\mathrm e}^{5 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 39 |
\begin{align*}
y^{\prime \prime }+y^{\prime }-2 y&=4 x^{2}+5 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 40 | \begin{align*}
y^{\prime \prime \prime }+2 y^{\prime \prime }-y^{\prime }-2 y&=4 \,{\mathrm e}^{2 x} \\
\end{align*} | ✓ | ✓ | ✓ | ✓ |
|
| Problem 41 |
\begin{align*}
y^{\prime \prime \prime }+y^{\prime \prime }-10 y^{\prime }+8 y&=24 \,{\mathrm e}^{-3 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 42 |
\begin{align*}
y^{\prime \prime \prime }+5 y^{\prime \prime }+6 y^{\prime }&=6 \,{\mathrm e}^{-x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| ID | problem | ODE | Solved? | Maple | Mma | Sympy |
| Problem 25 |
\begin{align*}
y^{\prime \prime }+y&=6 \,{\mathrm e}^{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 26 |
\begin{align*}
y^{\prime \prime }+4 y^{\prime }+4 y&=5 \,{\mathrm e}^{-2 x} x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 27 |
\begin{align*}
y^{\prime \prime }+4 y&=8 \sin \left (2 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 28 |
\begin{align*}
y^{\prime \prime }-y^{\prime }-2 y&=5 \,{\mathrm e}^{2 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 29 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }+5 y&=3 \sin \left (2 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 30 |
\begin{align*}
y^{\prime \prime \prime }+2 y^{\prime \prime }-5 y^{\prime }-6 y&=4 x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 31 |
\begin{align*}
y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y&=9 \,{\mathrm e}^{-x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 32 |
\begin{align*}
y^{\prime \prime \prime }+3 y^{\prime \prime }+3 y^{\prime }+y&=2 \,{\mathrm e}^{-x}+3 \,{\mathrm e}^{2 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 33 |
\begin{align*}
y^{\prime \prime }+9 y&=5 \cos \left (2 x \right ) \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 34 |
\begin{align*}
y^{\prime \prime }-y&=9 x \,{\mathrm e}^{2 x} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 7 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 35 |
\begin{align*}
y^{\prime \prime }+y^{\prime }-2 y&=-10 \sin \left (x \right ) \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 36 |
\begin{align*}
y^{\prime \prime }+y^{\prime }-2 y&=4 \cos \left (x \right )-2 \sin \left (x \right ) \\
y \left (0\right ) &= -1 \\
y^{\prime }\left (0\right ) &= 4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 38 |
\begin{align*}
y^{\prime \prime }+\omega ^{2} y&=\frac {F_{0} \cos \left (\omega t \right )}{m} \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 39 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime }+6 y&=7 \,{\mathrm e}^{2 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 40 |
\begin{align*}
y^{\prime \prime \prime }+y^{\prime \prime }+y^{\prime }+y&=4 x \,{\mathrm e}^{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 41 |
\begin{align*}
y^{\prime \prime \prime \prime }+104 y^{\prime \prime \prime }+2740 y^{\prime \prime }&=5 \cos \left (3 x \right ) {\mathrm e}^{-2 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 46 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }-3 y&=\sin \left (x \right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 47 | \begin{align*}
y^{\prime \prime }+6 y&=\sin \left (x \right )^{2} \cos \left (x \right )^{2} \\
\end{align*} | ✓ | ✓ | ✓ | ✓ |
|
| ID | problem | ODE | Solved? | Maple | Mma | Sympy |
| Problem 1 |
\begin{align*}
y^{\prime \prime }-16 y&=20 \cos \left (4 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 2 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }+y&=50 \sin \left (3 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 3 |
\begin{align*}
y^{\prime \prime }-y&=10 \,{\mathrm e}^{2 x} \cos \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 4 |
\begin{align*}
y^{\prime \prime }+4 y^{\prime }+4 y&=169 \sin \left (3 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 5 |
\begin{align*}
y^{\prime \prime }-y^{\prime }-2 y&=40 \sin \left (x \right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 6 |
\begin{align*}
y^{\prime \prime }+y&=3 \,{\mathrm e}^{x} \cos \left (2 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 7 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }+2 y&=2 \,{\mathrm e}^{-x} \sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 8 |
\begin{align*}
y^{\prime \prime }-4 y&=100 \,{\mathrm e}^{x} \sin \left (x \right ) x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 9 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }+5 y&=4 \,{\mathrm e}^{-x} \cos \left (2 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 10 |
\begin{align*}
y^{\prime \prime }-2 y^{\prime }+10 y&=24 \,{\mathrm e}^{x} \cos \left (3 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 11 |
\begin{align*}
y^{\prime \prime }+16 y&=34 \,{\mathrm e}^{x}+16 \cos \left (4 x \right )-8 \sin \left (4 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| ID | problem | ODE | Solved? | Maple | Mma | Sympy |
| Problem 1 |
\begin{align*}
y^{\prime \prime }-6 y^{\prime }+9 y&=4 \,{\mathrm e}^{3 x} \ln \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 2 |
\begin{align*}
y^{\prime \prime }+4 y^{\prime }+4 y&=\frac {{\mathrm e}^{-2 x}}{x^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 3 |
\begin{align*}
y^{\prime \prime }+9 y&=18 \sec \left (3 x \right )^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 4 |
\begin{align*}
y^{\prime \prime }+6 y^{\prime }+9 y&=\frac {2 \,{\mathrm e}^{-3 x}}{x^{2}+1} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| Problem 5 |
\begin{align*}
y^{\prime \prime }-4 y&=\frac {8}{{\mathrm e}^{2 x}+1} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 6 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime }+5 y&={\mathrm e}^{2 x} \tan \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 7 |
\begin{align*}
y^{\prime \prime }+9 y&=\frac {36}{4-\cos \left (3 x \right )^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 8 |
\begin{align*}
y^{\prime \prime }-10 y^{\prime }+25 y&=\frac {2 \,{\mathrm e}^{5 x}}{x^{2}+4} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| Problem 9 |
\begin{align*}
y^{\prime \prime }-6 y^{\prime }+13 y&=4 \,{\mathrm e}^{3 x} \sec \left (2 x \right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 10 |
\begin{align*}
y^{\prime \prime }+y&=\sec \left (x \right )+4 \,{\mathrm e}^{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 11 |
\begin{align*}
y^{\prime \prime }+y&=\csc \left (x \right )+2 x^{2}+5 x +1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 12 |
\begin{align*}
y^{\prime \prime }-y&=2 \tanh \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 13 |
\begin{align*}
y^{\prime \prime }-2 m y^{\prime }+m^{2} y&=\frac {{\mathrm e}^{m x}}{x^{2}+1} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| Problem 13 |
\begin{align*}
y^{\prime \prime }-2 y^{\prime }+y&=\frac {4 \,{\mathrm e}^{x} \ln \left (x \right )}{x^{3}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 15 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }+y&=\frac {{\mathrm e}^{-x}}{\sqrt {-x^{2}+4}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 16 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }+17 y&=\frac {64 \,{\mathrm e}^{-x}}{3+\sin \left (4 x \right )^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| Problem 17 |
\begin{align*}
y^{\prime \prime }+4 y^{\prime }+4 y&=\frac {4 \,{\mathrm e}^{-2 x}}{x^{2}+1}+2 x^{2}-1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| Problem 18 | \begin{align*}
y^{\prime \prime }+4 y^{\prime }+4 y&=15 \,{\mathrm e}^{-2 x} \ln \left (x \right )+25 \cos \left (x \right ) \\
\end{align*} | ✓ | ✓ | ✓ | ✓ |
|
| Problem 19 |
\begin{align*}
y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y&=\frac {2 \,{\mathrm e}^{x}}{x^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 20 |
\begin{align*}
y^{\prime \prime \prime }-6 y^{\prime \prime }+12 y^{\prime }-8 y&=36 \,{\mathrm e}^{2 x} \ln \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 21 |
\begin{align*}
y^{\prime \prime \prime }+3 y^{\prime \prime }+3 y^{\prime }+y&=\frac {2 \,{\mathrm e}^{-x}}{x^{2}+1} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| Problem 22 |
\begin{align*}
y^{\prime \prime \prime }-6 y^{\prime \prime }+9 y^{\prime }&=12 \,{\mathrm e}^{3 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 23 |
\begin{align*}
y^{\prime \prime }-9 y&=F \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 24 |
\begin{align*}
y^{\prime \prime }+5 y^{\prime }+4 y&=F \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 25 |
\begin{align*}
y^{\prime \prime }+y^{\prime }-2 y&=F \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 26 |
\begin{align*}
y^{\prime \prime }+4 y^{\prime }-12 y&=F \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 27 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime }+4 y&=5 x \,{\mathrm e}^{2 x} \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 28 |
\begin{align*}
y^{\prime \prime }+y&=\sec \left (x \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| ID | problem | ODE | Solved? | Maple | Mma | Sympy |
| Problem 14 |
\begin{align*}
x^{2} y^{\prime \prime }+4 x y^{\prime }+2 y&=4 \ln \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 15 |
\begin{align*}
x^{2} y^{\prime \prime }+4 x y^{\prime }+2 y&=\cos \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 16 |
\begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }+9 y&=9 \ln \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 17 |
\begin{align*}
x^{2} y^{\prime \prime }-x y^{\prime }+5 y&=8 x \ln \left (x \right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 18 |
\begin{align*}
x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y&=x^{4} \sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 19 |
\begin{align*}
x^{2} y^{\prime \prime }+6 x y^{\prime }+6 y&=4 \,{\mathrm e}^{2 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 20 |
\begin{align*}
x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y&=\frac {x^{2}}{\ln \left (x \right )} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 21 |
\begin{align*}
x^{2} y^{\prime \prime }-\left (2 m -1\right ) x y^{\prime }+m^{2} y&=x^{m} \ln \left (x \right )^{k} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 22 |
\begin{align*}
x^{2} y^{\prime \prime }-x y^{\prime }+5 y&=0 \\
y \left (1\right ) &= \sqrt {2} \\
y^{\prime }\left (1\right ) &= 3 \sqrt {2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 23 |
\begin{align*}
t^{2} y^{\prime \prime }+t y^{\prime }+25 y&=0 \\
y \left (1\right ) &= \frac {3 \sqrt {3}}{2} \\
y^{\prime }\left (1\right ) &= {\frac {15}{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| ID | problem | ODE | Solved? | Maple | Mma | Sympy |
| Problem 1 |
\begin{align*}
x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 2 |
\begin{align*}
x y^{\prime \prime }+\left (1-2 x \right ) y^{\prime }+\left (x -1\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| Problem 3 |
\begin{align*}
x^{2} y^{\prime \prime }-2 x y^{\prime }+\left (x^{2}+2\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 4 |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| Problem 5 |
\begin{align*}
y^{\prime \prime }-\frac {y^{\prime }}{x}+4 x^{2} y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 6 |
\begin{align*}
4 x^{2} y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}-1\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 10 |
\begin{align*}
y^{\prime \prime }+y&=\csc \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 11 |
\begin{align*}
x y^{\prime \prime }-\left (2 x +1\right ) y^{\prime }+2 y&=8 x^{2} {\mathrm e}^{2 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| Problem 12 |
\begin{align*}
x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y&=8 x^{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 13 |
\begin{align*}
y^{\prime \prime }-6 y^{\prime }+9 y&=15 \,{\mathrm e}^{3 x} \sqrt {x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 14 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime }+4 y&=4 \,{\mathrm e}^{2 x} \ln \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 15 |
\begin{align*}
4 x^{2} y^{\prime \prime }+y&=\sqrt {x}\, \ln \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| ID | problem | ODE | Solved? | Maple | Mma | Sympy |
| Problem 7 |
\begin{align*}
y^{\prime \prime \prime }+3 y^{\prime \prime }-4 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 8 |
\begin{align*}
y^{\prime \prime \prime }+11 y^{\prime \prime }+36 y^{\prime }+26 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 18 |
\begin{align*}
y^{\prime \prime }+6 y^{\prime }+9 y&=4 \,{\mathrm e}^{-3 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 19 |
\begin{align*}
y^{\prime \prime }+6 y^{\prime }+9 y&=4 \,{\mathrm e}^{-2 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 20 |
\begin{align*}
y^{\prime \prime \prime }-6 y^{\prime \prime }+25 y^{\prime }&=x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 21 |
\begin{align*}
y^{\prime \prime \prime }-6 y^{\prime \prime }+25 y^{\prime }&=\sin \left (4 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 22 |
\begin{align*}
y^{\prime \prime \prime }+9 y^{\prime \prime }+24 y^{\prime }+16 y&=8 \,{\mathrm e}^{-x}+1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 27 |
\begin{align*}
y^{\prime \prime }-4 y&=5 \,{\mathrm e}^{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 28 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }+y&=2 x \,{\mathrm e}^{-x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 29 |
\begin{align*}
y^{\prime \prime }-y&=4 \,{\mathrm e}^{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 30 |
\begin{align*}
y^{\prime \prime }+y x&=\sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 31 |
\begin{align*}
y^{\prime \prime }+4 y&=\ln \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 32 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }-3 y&=5 \,{\mathrm e}^{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 33 |
\begin{align*}
y^{\prime \prime }+y&=\tan \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 34 |
\begin{align*}
y^{\prime \prime }+y&=4 \cos \left (2 x \right )+3 \,{\mathrm e}^{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| ID | problem | ODE | Solved? | Maple | Mma | Sympy |
| 1 |
\begin{align*}
x_{1}^{\prime }\left (t \right )&=2 x_{1} \left (t \right )+x_{2} \left (t \right ) \\
x_{2}^{\prime }\left (t \right )&=2 x_{1} \left (t \right )+3 x_{2} \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 2 |
\begin{align*}
x_{1}^{\prime }\left (t \right )&=2 x_{1} \left (t \right )-3 x_{2} \left (t \right ) \\
x_{2}^{\prime }\left (t \right )&=x_{1} \left (t \right )-2 x_{2} \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 3 |
\begin{align*}
x_{1}^{\prime }\left (t \right )&=4 x_{1} \left (t \right )+2 x_{2} \left (t \right ) \\
x_{2}^{\prime }\left (t \right )&=-x_{1} \left (t \right )+x_{2} \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 4 |
\begin{align*}
x_{1}^{\prime }\left (t \right )&=2 x_{1} \left (t \right )+4 x_{2} \left (t \right ) \\
x_{2}^{\prime }\left (t \right )&=-4 x_{1} \left (t \right )-6 x_{2} \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 5 |
\begin{align*}
x_{1}^{\prime }\left (t \right )&=2 x_{2} \left (t \right ) \\
x_{2}^{\prime }\left (t \right )&=-2 x_{1} \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 6 |
\begin{align*}
x_{1}^{\prime }\left (t \right )&=x_{1} \left (t \right )-3 x_{2} \left (t \right ) \\
x_{2}^{\prime }\left (t \right )&=3 x_{1} \left (t \right )+x_{2} \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 7 |
\begin{align*}
x_{1}^{\prime }\left (t \right )&=2 x_{1} \left (t \right ) \\
x_{2}^{\prime }\left (t \right )&=x_{2} \left (t \right )-x_{3} \left (t \right ) \\
x_{3}^{\prime }\left (t \right )&=x_{2} \left (t \right )+x_{3} \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 8 |
\begin{align*}
x_{1}^{\prime }\left (t \right )&=-2 x_{1} \left (t \right )+x_{2} \left (t \right )+x_{3} \left (t \right ) \\
x_{2}^{\prime }\left (t \right )&=x_{1} \left (t \right )-x_{2} \left (t \right )+3 x_{3} \left (t \right ) \\
x_{3}^{\prime }\left (t \right )&=-x_{2} \left (t \right )-3 x_{3} \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 9 |
\begin{align*}
x_{1}^{\prime }\left (t \right )&=2 x_{2} \left (t \right ) \\
x_{2}^{\prime }\left (t \right )&=x_{1} \left (t \right )+x_{2} \left (t \right ) \\
\end{align*} With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 3 \\
x_{2} \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 10 |
\begin{align*}
x_{1}^{\prime }\left (t \right )&=2 x_{1} \left (t \right )+5 x_{2} \left (t \right ) \\
x_{2}^{\prime }\left (t \right )&=-x_{1} \left (t \right )-2 x_{2} \left (t \right ) \\
\end{align*} With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 0 \\
x_{2} \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 11 |
\begin{align*}
x_{1}^{\prime }\left (t \right )&=2 x_{1} \left (t \right )+x_{2} \left (t \right ) \\
x_{2}^{\prime }\left (t \right )&=-x_{1} \left (t \right )+4 x_{2} \left (t \right ) \\
\end{align*} With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 1 \\
x_{2} \left (0\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 12 |
\begin{align*}
x_{1}^{\prime }\left (t \right )&=x_{1} \left (t \right )+2 x_{2} \left (t \right )+5 \,{\mathrm e}^{4 t} \\
x_{2}^{\prime }\left (t \right )&=2 x_{1} \left (t \right )+x_{2} \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 13 |
\begin{align*}
x_{1}^{\prime }\left (t \right )&=-2 x_{1} \left (t \right )+x_{2} \left (t \right )+t \\
x_{2}^{\prime }\left (t \right )&=-2 x_{1} \left (t \right )+x_{2} \left (t \right )+1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 14 |
\begin{align*}
x_{1}^{\prime }\left (t \right )&=x_{1} \left (t \right )+x_{2} \left (t \right )+{\mathrm e}^{2 t} \\
x_{2}^{\prime }\left (t \right )&=3 x_{1} \left (t \right )-x_{2} \left (t \right )+5 \,{\mathrm e}^{2 t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 21 |
\begin{align*}
x_{1}^{\prime }\left (t \right )&=-\tan \left (t \right ) x_{1} \left (t \right )+3 \cos \left (t \right )^{2} \\
x_{2}^{\prime }\left (t \right )&=x_{1} \left (t \right )+\tan \left (t \right ) x_{2} \left (t \right )+2 \sin \left (t \right ) \\
\end{align*} With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 4 \\
x_{2} \left (0\right ) &= 0 \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
|
| ID | problem | ODE | Solved? | Maple | Mma | Sympy |
| 12 |
\begin{align*}
x_{1}^{\prime }\left (t \right )&=2 x_{1} \left (t \right )-4 x_{2} \left (t \right ) \\
x_{2}^{\prime }\left (t \right )&=x_{1} \left (t \right )-3 x_{2} \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 13 |
\begin{align*}
x_{1}^{\prime }\left (t \right )&=x_{2} \left (t \right ) \\
x_{2}^{\prime }\left (t \right )&=-b x_{1} \left (t \right )-a x_{2} \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| ID | problem | ODE | Solved? | Maple | Mma | Sympy |
| 1 |
\begin{align*}
x_{1}^{\prime }\left (t \right )&=3 x_{2} \left (t \right ) \\
x_{2}^{\prime }\left (t \right )&=-3 x_{1} \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 2 |
\begin{align*}
x_{1}^{\prime }\left (t \right )&=-2 x_{1} \left (t \right )+3 x_{2} \left (t \right ) \\
x_{2}^{\prime }\left (t \right )&=-2 x_{1} \left (t \right )+5 x_{2} \left (t \right ) \\
\end{align*} With initial conditions \begin{align*}
x_{1} \left (0\right ) &= -2 \\
x_{2} \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 3 |
\begin{align*}
x_{1}^{\prime }\left (t \right )&=x_{1} \left (t \right )-2 x_{2} \left (t \right ) \\
x_{2}^{\prime }\left (t \right )&=2 x_{1} \left (t \right )+x_{2} \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 4 |
\begin{align*}
x_{1}^{\prime }\left (t \right )&=3 x_{1} \left (t \right )+x_{2} \left (t \right ) \\
x_{2}^{\prime }\left (t \right )&=-x_{1} \left (t \right )+x_{2} \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 5 |
\begin{align*}
x_{1}^{\prime }\left (t \right )&=2 x_{1} \left (t \right )-x_{2} \left (t \right )+3 x_{3} \left (t \right ) \\
x_{2}^{\prime }\left (t \right )&=3 x_{1} \left (t \right )+x_{2} \left (t \right ) \\
x_{3}^{\prime }\left (t \right )&=2 x_{1} \left (t \right )-x_{2} \left (t \right )+3 x_{3} \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 6 |
\begin{align*}
x_{1}^{\prime }\left (t \right )&=\frac {x_{1} \left (t \right )}{t} \\
x_{2}^{\prime }\left (t \right )&=x_{2} \left (t \right ) \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
|
| 7 |
\begin{align*}
x_{1}^{\prime }\left (t \right )&=\frac {x_{1} \left (t \right )}{t}+x_{2} \left (t \right ) t \\
x_{2}^{\prime }\left (t \right )&=-\frac {x_{1} \left (t \right )}{t} \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
|
| ID | problem | ODE | Solved? | Maple | Mma | Sympy |
| 1 |
\begin{align*}
x_{1}^{\prime }\left (t \right )&=-x_{1} \left (t \right )+2 x_{2} \left (t \right ) \\
x_{2}^{\prime }\left (t \right )&=2 x_{1} \left (t \right )+2 x_{2} \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 2 |
\begin{align*}
x_{1}^{\prime }\left (t \right )&=-2 x_{1} \left (t \right )-7 x_{2} \left (t \right ) \\
x_{2}^{\prime }\left (t \right )&=-x_{1} \left (t \right )+4 x_{2} \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 3 |
\begin{align*}
x_{1}^{\prime }\left (t \right )&=-4 x_{2} \left (t \right ) \\
x_{2}^{\prime }\left (t \right )&=4 x_{1} \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 4 |
\begin{align*}
x_{1}^{\prime }\left (t \right )&=x_{1} \left (t \right )-2 x_{2} \left (t \right ) \\
x_{2}^{\prime }\left (t \right )&=5 x_{1} \left (t \right )-5 x_{2} \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 5 |
\begin{align*}
x_{1}^{\prime }\left (t \right )&=-x_{1} \left (t \right )+2 x_{2} \left (t \right ) \\
x_{2}^{\prime }\left (t \right )&=-2 x_{1} \left (t \right )-x_{2} \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 6 |
\begin{align*}
x_{1}^{\prime }\left (t \right )&=2 x_{1} \left (t \right ) \\
x_{2}^{\prime }\left (t \right )&=5 x_{2} \left (t \right )-7 x_{3} \left (t \right ) \\
x_{3}^{\prime }\left (t \right )&=2 x_{2} \left (t \right )-4 x_{3} \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 7 |
\begin{align*}
x_{1}^{\prime }\left (t \right )&=-x_{1} \left (t \right ) \\
x_{2}^{\prime }\left (t \right )&=x_{1} \left (t \right )+5 x_{2} \left (t \right )-x_{3} \left (t \right ) \\
x_{3}^{\prime }\left (t \right )&=x_{1} \left (t \right )+6 x_{2} \left (t \right )-2 x_{3} \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 8 |
\begin{align*}
x_{1}^{\prime }\left (t \right )&=x_{2} \left (t \right ) \\
x_{2}^{\prime }\left (t \right )&=-x_{1} \left (t \right ) \\
x_{3}^{\prime }\left (t \right )&=5 x_{3} \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 9 |
\begin{align*}
x_{1}^{\prime }\left (t \right )&=2 x_{1} \left (t \right )+3 x_{3} \left (t \right ) \\
x_{2}^{\prime }\left (t \right )&=-4 x_{2} \left (t \right ) \\
x_{3}^{\prime }\left (t \right )&=-3 x_{1} \left (t \right )+2 x_{3} \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 10 |
\begin{align*}
x_{1}^{\prime }\left (t \right )&=3 x_{1} \left (t \right )+2 x_{2} \left (t \right )+6 x_{3} \left (t \right ) \\
x_{2}^{\prime }\left (t \right )&=-2 x_{1} \left (t \right )+x_{2} \left (t \right )-2 x_{3} \left (t \right ) \\
x_{3}^{\prime }\left (t \right )&=-x_{1} \left (t \right )-2 x_{2} \left (t \right )-4 x_{3} \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 11 |
\begin{align*}
x_{1}^{\prime }\left (t \right )&=-3 x_{2} \left (t \right )+x_{3} \left (t \right ) \\
x_{2}^{\prime }\left (t \right )&=-2 x_{1} \left (t \right )-x_{2} \left (t \right )+x_{3} \left (t \right ) \\
x_{3}^{\prime }\left (t \right )&=2 x_{3} \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 12 |
\begin{align*}
x_{1}^{\prime }\left (t \right )&=3 x_{1} \left (t \right )-x_{3} \left (t \right ) \\
x_{2}^{\prime }\left (t \right )&=-3 x_{2} \left (t \right )-x_{3} \left (t \right ) \\
x_{3}^{\prime }\left (t \right )&=2 x_{2} \left (t \right )-x_{3} \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 13 |
\begin{align*}
x_{1}^{\prime }\left (t \right )&=x_{1} \left (t \right )+x_{2} \left (t \right )-x_{3} \left (t \right ) \\
x_{2}^{\prime }\left (t \right )&=x_{1} \left (t \right )+x_{2} \left (t \right )+x_{3} \left (t \right ) \\
x_{3}^{\prime }\left (t \right )&=-x_{1} \left (t \right )+x_{2} \left (t \right )+x_{3} \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 14 |
\begin{align*}
x_{1}^{\prime }\left (t \right )&=2 x_{1} \left (t \right )-x_{2} \left (t \right )+3 x_{3} \left (t \right ) \\
x_{2}^{\prime }\left (t \right )&=2 x_{1} \left (t \right )-x_{2} \left (t \right )+3 x_{3} \left (t \right ) \\
x_{3}^{\prime }\left (t \right )&=2 x_{1} \left (t \right )-x_{2} \left (t \right )+3 x_{3} \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 15 |
\begin{align*}
x_{1}^{\prime }\left (t \right )&=x_{1} \left (t \right )+2 x_{2} \left (t \right )+3 x_{3} \left (t \right )+4 x_{4} \left (t \right ) \\
x_{2}^{\prime }\left (t \right )&=4 x_{1} \left (t \right )+3 x_{2} \left (t \right )+2 x_{3} \left (t \right )+x_{4} \left (t \right ) \\
x_{3}^{\prime }\left (t \right )&=4 x_{1} \left (t \right )+5 x_{2} \left (t \right )+6 x_{3} \left (t \right )+7 x_{4} \left (t \right ) \\
x_{4}^{\prime }\left (t \right )&=7 x_{1} \left (t \right )+6 x_{2} \left (t \right )+5 x_{3} \left (t \right )+4 x_{4} \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 16 |
\begin{align*}
x_{1}^{\prime }\left (t \right )&=x_{2} \left (t \right ) \\
x_{2}^{\prime }\left (t \right )&=-x_{1} \left (t \right ) \\
x_{3}^{\prime }\left (t \right )&=-x_{4} \left (t \right ) \\
x_{4}^{\prime }\left (t \right )&=x_{3} \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 17 |
\begin{align*}
x_{1}^{\prime }\left (t \right )&=-x_{1} \left (t \right )+4 x_{2} \left (t \right ) \\
x_{2}^{\prime }\left (t \right )&=2 x_{1} \left (t \right )-3 x_{2} \left (t \right ) \\
\end{align*} With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 3 \\
x_{2} \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 18 | \begin{align*}
x_{1}^{\prime }\left (t \right )&=-x_{1} \left (t \right )-6 x_{2} \left (t \right ) \\
x_{2}^{\prime }\left (t \right )&=3 x_{1} \left (t \right )+5 x_{2} \left (t \right ) \\
\end{align*} With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 2 \\
x_{2} \left (0\right ) &= 2 \\
\end{align*} | ✓ | ✓ | ✓ | ✓ |
|
| 19 |
\begin{align*}
x_{1}^{\prime }\left (t \right )&=2 x_{1} \left (t \right )-x_{2} \left (t \right )+3 x_{3} \left (t \right ) \\
x_{2}^{\prime }\left (t \right )&=3 x_{1} \left (t \right )+x_{2} \left (t \right ) \\
x_{3}^{\prime }\left (t \right )&=2 x_{1} \left (t \right )-x_{2} \left (t \right )+3 x_{3} \left (t \right ) \\
\end{align*} With initial conditions \begin{align*}
x_{1} \left (0\right ) &= -4 \\
x_{2} \left (0\right ) &= 4 \\
x_{3} \left (0\right ) &= 4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 20 |
\begin{align*}
x_{1}^{\prime }\left (t \right )&=4 x_{2} \left (t \right ) \\
x_{2}^{\prime }\left (t \right )&=-4 x_{1} \left (t \right ) \\
\end{align*} With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 1 \\
x_{2} \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 28 |
\begin{align*}
x_{1}^{\prime }\left (t \right )&=x_{2} \left (t \right ) \\
x_{2}^{\prime }\left (t \right )&=-b x_{1} \left (t \right )-a x_{2} \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| ID | problem | ODE | Solved? | Maple | Mma | Sympy |
| 1 |
\begin{align*}
x_{1}^{\prime }\left (t \right )&=x_{1} \left (t \right )+x_{2} \left (t \right ) \\
x_{2}^{\prime }\left (t \right )&=-x_{1} \left (t \right )+3 x_{2} \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 2 |
\begin{align*}
x_{1}^{\prime }\left (t \right )&=-2 x_{2} \left (t \right ) \\
x_{2}^{\prime }\left (t \right )&=2 x_{1} \left (t \right )+4 x_{2} \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 3 |
\begin{align*}
x_{1}^{\prime }\left (t \right )&=-3 x_{1} \left (t \right )-2 x_{2} \left (t \right ) \\
x_{2}^{\prime }\left (t \right )&=2 x_{1} \left (t \right )+x_{2} \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 4 |
\begin{align*}
x_{1}^{\prime }\left (t \right )&=x_{2} \left (t \right ) \\
x_{2}^{\prime }\left (t \right )&=x_{3} \left (t \right ) \\
x_{3}^{\prime }\left (t \right )&=x_{1} \left (t \right )+x_{2} \left (t \right )-x_{3} \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 5 |
\begin{align*}
x_{1}^{\prime }\left (t \right )&=2 x_{1} \left (t \right )+2 x_{2} \left (t \right )-x_{3} \left (t \right ) \\
x_{2}^{\prime }\left (t \right )&=2 x_{1} \left (t \right )+x_{2} \left (t \right )-x_{3} \left (t \right ) \\
x_{3}^{\prime }\left (t \right )&=2 x_{1} \left (t \right )+3 x_{2} \left (t \right )-x_{3} \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 6 |
\begin{align*}
x_{1}^{\prime }\left (t \right )&=-2 x_{1} \left (t \right ) \\
x_{2}^{\prime }\left (t \right )&=x_{1} \left (t \right )-3 x_{2} \left (t \right )-x_{3} \left (t \right ) \\
x_{3}^{\prime }\left (t \right )&=-x_{1} \left (t \right )+x_{2} \left (t \right )-x_{3} \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 7 |
\begin{align*}
x_{1}^{\prime }\left (t \right )&=15 x_{1} \left (t \right )-32 x_{2} \left (t \right )+12 x_{3} \left (t \right ) \\
x_{2}^{\prime }\left (t \right )&=8 x_{1} \left (t \right )-17 x_{2} \left (t \right )+6 x_{3} \left (t \right ) \\
x_{3}^{\prime }\left (t \right )&=-x_{3} \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 8 |
\begin{align*}
x_{1}^{\prime }\left (t \right )&=4 x_{1} \left (t \right ) \\
x_{2}^{\prime }\left (t \right )&=x_{1} \left (t \right )+4 x_{2} \left (t \right ) \\
x_{3}^{\prime }\left (t \right )&=x_{2} \left (t \right )+4 x_{3} \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 9 |
\begin{align*}
x_{1}^{\prime }\left (t \right )&=x_{1} \left (t \right ) \\
x_{2}^{\prime }\left (t \right )&=3 x_{2} \left (t \right )+2 x_{3} \left (t \right ) \\
x_{3}^{\prime }\left (t \right )&=2 x_{1} \left (t \right )-2 x_{2} \left (t \right )-x_{3} \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 10 |
\begin{align*}
x_{1}^{\prime }\left (t \right )&=3 x_{1} \left (t \right )+x_{2} \left (t \right ) \\
x_{2}^{\prime }\left (t \right )&=-x_{1} \left (t \right )+5 x_{2} \left (t \right ) \\
x_{3}^{\prime }\left (t \right )&=4 x_{3} \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 11 |
\begin{align*}
x_{1}^{\prime }\left (t \right )&=-x_{1} \left (t \right )+x_{2} \left (t \right ) \\
x_{2}^{\prime }\left (t \right )&=-2 x_{1} \left (t \right )-3 x_{2} \left (t \right )+x_{3} \left (t \right ) \\
x_{3}^{\prime }\left (t \right )&=x_{1} \left (t \right )+x_{2} \left (t \right )-2 x_{3} \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 12 |
\begin{align*}
x_{1}^{\prime }\left (t \right )&=-x_{2} \left (t \right ) \\
x_{2}^{\prime }\left (t \right )&=x_{1} \left (t \right ) \\
x_{3}^{\prime }\left (t \right )&=x_{1} \left (t \right )+2 x_{3} \left (t \right )+x_{4} \left (t \right ) \\
x_{4}^{\prime }\left (t \right )&=x_{2} \left (t \right )+2 x_{4} \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 13 |
\begin{align*}
x_{1}^{\prime }\left (t \right )&=-2 x_{1} \left (t \right )+3 x_{2} \left (t \right ) \\
x_{2}^{\prime }\left (t \right )&=3 x_{1} \left (t \right )-2 x_{2} \left (t \right ) \\
x_{3}^{\prime }\left (t \right )&=x_{1} \left (t \right )+x_{3} \left (t \right )+x_{4} \left (t \right ) \\
x_{4}^{\prime }\left (t \right )&=x_{2} \left (t \right )+x_{4} \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 14 |
\begin{align*}
x_{1}^{\prime }\left (t \right )&=-x_{2} \left (t \right ) \\
x_{2}^{\prime }\left (t \right )&=x_{1} \left (t \right ) \\
x_{3}^{\prime }\left (t \right )&=x_{1} \left (t \right )-x_{4} \left (t \right ) \\
x_{4}^{\prime }\left (t \right )&=x_{2} \left (t \right )+x_{3} \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 15 |
\begin{align*}
x_{1}^{\prime }\left (t \right )&=-2 x_{1} \left (t \right )-x_{2} \left (t \right ) \\
x_{2}^{\prime }\left (t \right )&=x_{1} \left (t \right )-4 x_{2} \left (t \right ) \\
\end{align*} With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 0 \\
x_{2} \left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 16 |
\begin{align*}
x_{1}^{\prime }\left (t \right )&=-2 x_{1} \left (t \right )-x_{2} \left (t \right )+4 x_{3} \left (t \right ) \\
x_{2}^{\prime }\left (t \right )&=-x_{2} \left (t \right ) \\
x_{3}^{\prime }\left (t \right )&=-x_{1} \left (t \right )-3 x_{2} \left (t \right )+2 x_{3} \left (t \right ) \\
\end{align*} With initial conditions \begin{align*}
x_{1} \left (0\right ) &= -2 \\
x_{2} \left (0\right ) &= 1 \\
x_{3} \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| ID | problem | ODE | Solved? | Maple | Mma | Sympy |
| 1 |
\begin{align*}
x_{1}^{\prime }\left (t \right )&=4 x_{1} \left (t \right )-3 x_{2} \left (t \right )+{\mathrm e}^{2 t} \\
x_{2}^{\prime }\left (t \right )&=2 x_{1} \left (t \right )-x_{2} \left (t \right )+{\mathrm e}^{t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 2 |
\begin{align*}
x_{1}^{\prime }\left (t \right )&=2 x_{1} \left (t \right )-x_{2} \left (t \right ) \\
x_{2}^{\prime }\left (t \right )&=-x_{1} \left (t \right )+2 x_{2} \left (t \right )+4 \,{\mathrm e}^{t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 3 |
\begin{align*}
x_{1}^{\prime }\left (t \right )&=3 x_{1} \left (t \right )+x_{2} \left (t \right )+t \,{\mathrm e}^{3 t} \\
x_{2}^{\prime }\left (t \right )&=3 x_{2} \left (t \right )+{\mathrm e}^{3 t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 4 |
\begin{align*}
x_{1}^{\prime }\left (t \right )&=-x_{1} \left (t \right )+x_{2} \left (t \right )+20 \,{\mathrm e}^{3 t} \\
x_{2}^{\prime }\left (t \right )&=3 x_{1} \left (t \right )+x_{2} \left (t \right )+12 \,{\mathrm e}^{t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 5 |
\begin{align*}
x_{1}^{\prime }\left (t \right )&=-x_{1} \left (t \right )+2 x_{2} \left (t \right )+54 t \,{\mathrm e}^{3 t} \\
x_{2}^{\prime }\left (t \right )&=-2 x_{1} \left (t \right )+4 x_{2} \left (t \right )+9 \,{\mathrm e}^{3 t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 6 |
\begin{align*}
x_{1}^{\prime }\left (t \right )&=2 x_{1} \left (t \right )+4 x_{2} \left (t \right )+8 \sin \left (2 t \right ) \\
x_{2}^{\prime }\left (t \right )&=-2 x_{1} \left (t \right )-2 x_{2} \left (t \right )+8 \cos \left (2 t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 7 |
\begin{align*}
x_{1}^{\prime }\left (t \right )&=3 x_{1} \left (t \right )+2 x_{2} \left (t \right )-3 \,{\mathrm e}^{t} \\
x_{2}^{\prime }\left (t \right )&=-2 x_{1} \left (t \right )-x_{2} \left (t \right )+6 \,{\mathrm e}^{t} t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 8 |
\begin{align*}
x_{1}^{\prime }\left (t \right )&=x_{1} \left (t \right )-{\mathrm e}^{t} \\
x_{2}^{\prime }\left (t \right )&=2 x_{1} \left (t \right )-3 x_{2} \left (t \right )+2 x_{3} \left (t \right )+6 \,{\mathrm e}^{-t} \\
x_{3}^{\prime }\left (t \right )&=x_{1} \left (t \right )-2 x_{2} \left (t \right )+2 x_{3} \left (t \right )+{\mathrm e}^{t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 9 |
\begin{align*}
x_{1}^{\prime }\left (t \right )&=-x_{1} \left (t \right )-2 x_{2} \left (t \right )+2 x_{3} \left (t \right )-{\mathrm e}^{3 t} \\
x_{2}^{\prime }\left (t \right )&=2 x_{1} \left (t \right )+4 x_{2} \left (t \right )-x_{3} \left (t \right )+4 \,{\mathrm e}^{3 t} \\
x_{3}^{\prime }\left (t \right )&=3 x_{3} \left (t \right )+3 \,{\mathrm e}^{3 t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 11 |
\begin{align*}
x_{1}^{\prime }\left (t \right )&=2 x_{1} \left (t \right )-3 x_{2} \left (t \right )+34 \sin \left (t \right ) \\
x_{2}^{\prime }\left (t \right )&=-4 x_{1} \left (t \right )-2 x_{2} \left (t \right )+17 \cos \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| ID | problem | ODE | Solved? | Maple | Mma | Sympy |
| 2 |
\begin{align*}
x_{1}^{\prime }\left (t \right )&=2 x_{1} \left (t \right )+x_{2} \left (t \right ) \\
x_{2}^{\prime }\left (t \right )&=2 x_{2} \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 3 |
\begin{align*}
x_{1}^{\prime }\left (t \right )&=x_{1} \left (t \right )+2 x_{2} \left (t \right ) \\
x_{2}^{\prime }\left (t \right )&=-x_{2} \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 4 |
\begin{align*}
x_{1}^{\prime }\left (t \right )&=3 x_{1} \left (t \right ) \\
x_{2}^{\prime }\left (t \right )&=3 x_{2} \left (t \right )-x_{3} \left (t \right ) \\
x_{3}^{\prime }\left (t \right )&=x_{2} \left (t \right )+x_{3} \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 5 |
\begin{align*}
x_{1}^{\prime }\left (t \right )&=-3 x_{1} \left (t \right )-2 x_{2} \left (t \right ) \\
x_{2}^{\prime }\left (t \right )&=2 x_{1} \left (t \right )+x_{2} \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 6 |
\begin{align*}
x_{1}^{\prime }\left (t \right )&=3 x_{1} \left (t \right )-x_{2} \left (t \right ) \\
x_{2}^{\prime }\left (t \right )&=4 x_{1} \left (t \right )-x_{2} \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 7 |
\begin{align*}
x_{1}^{\prime }\left (t \right )&=2 x_{1} \left (t \right ) \\
x_{2}^{\prime }\left (t \right )&=x_{2} \left (t \right )-8 x_{3} \left (t \right ) \\
x_{3}^{\prime }\left (t \right )&=2 x_{2} \left (t \right )-7 x_{3} \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 8 |
\begin{align*}
x_{1}^{\prime }\left (t \right )&=x_{2} \left (t \right )+3 x_{3} \left (t \right ) \\
x_{2}^{\prime }\left (t \right )&=2 x_{1} \left (t \right )+3 x_{2} \left (t \right )-2 x_{3} \left (t \right ) \\
x_{3}^{\prime }\left (t \right )&=2 x_{2} \left (t \right )+2 x_{3} \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 9 |
\begin{align*}
x_{1}^{\prime }\left (t \right )&=-8 x_{1} \left (t \right )+6 x_{2} \left (t \right )-3 x_{3} \left (t \right ) \\
x_{2}^{\prime }\left (t \right )&=-12 x_{1} \left (t \right )+10 x_{2} \left (t \right )-3 x_{3} \left (t \right ) \\
x_{3}^{\prime }\left (t \right )&=-2 x_{3} \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 10 |
\begin{align*}
x_{1}^{\prime }\left (t \right )&=x_{1} \left (t \right ) \\
x_{2}^{\prime }\left (t \right )&=6 x_{2} \left (t \right )-7 x_{3} \left (t \right )+3 x_{4} \left (t \right ) \\
x_{3}^{\prime }\left (t \right )&=3 x_{3} \left (t \right )-x_{4} \left (t \right ) \\
x_{4}^{\prime }\left (t \right )&=-4 x_{2} \left (t \right )+9 x_{3} \left (t \right )-3 x_{4} \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 11 |
\begin{align*}
x_{1}^{\prime }\left (t \right )&=-x_{2} \left (t \right ) \\
x_{2}^{\prime }\left (t \right )&=x_{1} \left (t \right ) \\
x_{3}^{\prime }\left (t \right )&=x_{2} \left (t \right )-x_{4} \left (t \right ) \\
x_{4}^{\prime }\left (t \right )&=x_{2} \left (t \right )+x_{3} \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| ID | problem | ODE | Solved? | Maple | Mma | Sympy |
| 1 |
\begin{align*}
x_{1}^{\prime }\left (t \right )&=\left (2 t -1\right ) x_{1} \left (t \right ) \\
x_{2}^{\prime }\left (t \right )&={\mathrm e}^{-t^{2}+t} x_{1} \left (t \right )+x_{2} \left (t \right ) \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
|
| 2 |
\begin{align*}
x_{1}^{\prime }\left (t \right )&=t \cot \left (t^{2}\right ) x_{1} \left (t \right )+\frac {t \cos \left (t^{2}\right ) x_{3} \left (t \right )}{2} \\
x_{2}^{\prime }\left (t \right )&=\frac {x_{2} \left (t \right )}{t}-x_{3} \left (t \right )+2-t \sin \left (t \right ) \\
x_{3}^{\prime }\left (t \right )&=\csc \left (t^{2}\right ) x_{1} \left (t \right )+x_{2} \left (t \right )-x_{3} \left (t \right )+1-\cos \left (t \right ) t \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
|
| 3 |
\begin{align*}
x_{1}^{\prime }\left (t \right )&=-6 x_{1} \left (t \right )+x_{2} \left (t \right ) \\
x_{2}^{\prime }\left (t \right )&=6 x_{1} \left (t \right )-5 x_{2} \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 4 |
\begin{align*}
x_{1}^{\prime }\left (t \right )&=9 x_{1} \left (t \right )-2 x_{2} \left (t \right ) \\
x_{2}^{\prime }\left (t \right )&=5 x_{1} \left (t \right )-2 x_{2} \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 5 |
\begin{align*}
x_{1}^{\prime }\left (t \right )&=10 x_{1} \left (t \right )-4 x_{2} \left (t \right ) \\
x_{2}^{\prime }\left (t \right )&=4 x_{1} \left (t \right )+2 x_{2} \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 6 |
\begin{align*}
x_{1}^{\prime }\left (t \right )&=-8 x_{1} \left (t \right )+5 x_{2} \left (t \right ) \\
x_{2}^{\prime }\left (t \right )&=-5 x_{1} \left (t \right )+2 x_{2} \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 7 |
\begin{align*}
x_{1}^{\prime }\left (t \right )&=3 x_{1} \left (t \right )+4 x_{3} \left (t \right ) \\
x_{2}^{\prime }\left (t \right )&=2 x_{2} \left (t \right ) \\
x_{3}^{\prime }\left (t \right )&=-4 x_{1} \left (t \right )-5 x_{3} \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 8 |
\begin{align*}
x_{1}^{\prime }\left (t \right )&=-3 x_{1} \left (t \right )-x_{2} \left (t \right ) \\
x_{2}^{\prime }\left (t \right )&=4 x_{1} \left (t \right )-7 x_{2} \left (t \right ) \\
x_{3}^{\prime }\left (t \right )&=6 x_{1} \left (t \right )+6 x_{2} \left (t \right )+4 x_{3} \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 9 |
\begin{align*}
x_{1}^{\prime }\left (t \right )&=3 x_{1} \left (t \right )+13 x_{2} \left (t \right ) \\
x_{2}^{\prime }\left (t \right )&=-x_{1} \left (t \right )-3 x_{2} \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 10 |
\begin{align*}
x_{1}^{\prime }\left (t \right )&=-3 x_{1} \left (t \right )-10 x_{2} \left (t \right ) \\
x_{2}^{\prime }\left (t \right )&=5 x_{1} \left (t \right )+11 x_{2} \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 11 |
\begin{align*}
x_{1}^{\prime }\left (t \right )&=-x_{1} \left (t \right )-5 x_{2} \left (t \right )+x_{3} \left (t \right ) \\
x_{2}^{\prime }\left (t \right )&=4 x_{1} \left (t \right )-9 x_{2} \left (t \right )-x_{3} \left (t \right ) \\
x_{3}^{\prime }\left (t \right )&=3 x_{3} \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 12 |
\begin{align*}
x_{1}^{\prime }\left (t \right )&=-4 x_{1} \left (t \right ) \\
x_{2}^{\prime }\left (t \right )&=2 x_{1} \left (t \right )+5 x_{2} \left (t \right )-9 x_{3} \left (t \right ) \\
x_{3}^{\prime }\left (t \right )&=5 x_{2} \left (t \right )-x_{3} \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 13 |
\begin{align*}
x_{1}^{\prime }\left (t \right )&=2 x_{1} \left (t \right )-2 x_{2} \left (t \right )+x_{3} \left (t \right ) \\
x_{2}^{\prime }\left (t \right )&=x_{1} \left (t \right )-4 x_{2} \left (t \right )+x_{3} \left (t \right ) \\
x_{3}^{\prime }\left (t \right )&=2 x_{1} \left (t \right )+2 x_{2} \left (t \right )-3 x_{3} \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 14 |
\begin{align*}
x_{1}^{\prime }\left (t \right )&=2 x_{1} \left (t \right )-4 x_{2} \left (t \right )+3 x_{3} \left (t \right ) \\
x_{2}^{\prime }\left (t \right )&=-9 x_{1} \left (t \right )-3 x_{2} \left (t \right )-9 x_{3} \left (t \right ) \\
x_{3}^{\prime }\left (t \right )&=4 x_{1} \left (t \right )+4 x_{2} \left (t \right )+3 x_{3} \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 15 |
\begin{align*}
x_{1}^{\prime }\left (t \right )&=-17 x_{1} \left (t \right )-42 x_{3} \left (t \right ) \\
x_{2}^{\prime }\left (t \right )&=-7 x_{1} \left (t \right )+4 x_{2} \left (t \right )-14 x_{3} \left (t \right ) \\
x_{3}^{\prime }\left (t \right )&=7 x_{1} \left (t \right )+18 x_{3} \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 16 |
\begin{align*}
x_{1}^{\prime }\left (t \right )&=-16 x_{1} \left (t \right )+30 x_{2} \left (t \right )-18 x_{3} \left (t \right ) \\
x_{2}^{\prime }\left (t \right )&=-8 x_{1} \left (t \right )+8 x_{2} \left (t \right )+16 x_{3} \left (t \right ) \\
x_{3}^{\prime }\left (t \right )&=8 x_{1} \left (t \right )-15 x_{2} \left (t \right )+9 x_{3} \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 17 |
\begin{align*}
x_{1}^{\prime }\left (t \right )&=-7 x_{1} \left (t \right )-6 x_{2} \left (t \right )-7 x_{3} \left (t \right ) \\
x_{2}^{\prime }\left (t \right )&=-3 x_{1} \left (t \right )-3 x_{2} \left (t \right )-3 x_{3} \left (t \right ) \\
x_{3}^{\prime }\left (t \right )&=7 x_{1} \left (t \right )+6 x_{2} \left (t \right )+7 x_{3} \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 18 | \begin{align*}
x_{1}^{\prime }\left (t \right )&=3 x_{1} \left (t \right )-x_{2} \left (t \right )-2 x_{3} \left (t \right ) \\
x_{2}^{\prime }\left (t \right )&=x_{1} \left (t \right )+6 x_{2} \left (t \right )+x_{3} \left (t \right ) \\
x_{3}^{\prime }\left (t \right )&=x_{1} \left (t \right )+6 x_{3} \left (t \right ) \\
\end{align*} | ✓ | ✓ | ✓ | ✓ |
|
| 19 |
\begin{align*}
x_{1}^{\prime }\left (t \right )&=-x_{1} \left (t \right )-4 x_{2} \left (t \right )-2 x_{3} \left (t \right ) \\
x_{2}^{\prime }\left (t \right )&=-4 x_{1} \left (t \right )-5 x_{2} \left (t \right )-6 x_{3} \left (t \right ) \\
x_{3}^{\prime }\left (t \right )&=4 x_{1} \left (t \right )+8 x_{2} \left (t \right )+7 x_{3} \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 20 |
\begin{align*}
x_{1}^{\prime }\left (t \right )&=7 x_{1} \left (t \right )-2 x_{2} \left (t \right )+2 x_{3} \left (t \right ) \\
x_{2}^{\prime }\left (t \right )&=4 x_{2} \left (t \right )-x_{3} \left (t \right ) \\
x_{3}^{\prime }\left (t \right )&=-x_{1} \left (t \right )+x_{2} \left (t \right )+4 x_{3} \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 21 |
\begin{align*}
x_{1}^{\prime }\left (t \right )&=-3 x_{1} \left (t \right )-x_{2} \left (t \right )-2 x_{3} \left (t \right ) \\
x_{2}^{\prime }\left (t \right )&=x_{1} \left (t \right )+x_{3} \left (t \right ) \\
x_{3}^{\prime }\left (t \right )&=x_{1} \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 22 |
\begin{align*}
x_{1}^{\prime }\left (t \right )&=-2 x_{1} \left (t \right )-x_{3} \left (t \right ) \\
x_{2}^{\prime }\left (t \right )&=-x_{2} \left (t \right ) \\
x_{3}^{\prime }\left (t \right )&=x_{1} \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 23 |
\begin{align*}
x_{1}^{\prime }\left (t \right )&=2 x_{1} \left (t \right )+13 x_{2} \left (t \right ) \\
x_{2}^{\prime }\left (t \right )&=-x_{1} \left (t \right )-2 x_{2} \left (t \right ) \\
x_{3}^{\prime }\left (t \right )&=2 x_{3} \left (t \right )+4 x_{4} \left (t \right ) \\
x_{4}^{\prime }\left (t \right )&=2 x_{4} \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 24 |
\begin{align*}
x_{1}^{\prime }\left (t \right )&=7 x_{1} \left (t \right )-x_{4} \left (t \right ) \\
x_{2}^{\prime }\left (t \right )&=6 x_{2} \left (t \right ) \\
x_{3}^{\prime }\left (t \right )&=-x_{3} \left (t \right ) \\
x_{4}^{\prime }\left (t \right )&=2 x_{1} \left (t \right )+5 x_{4} \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 25 |
\begin{align*}
x_{1}^{\prime }\left (t \right )&=-6 x_{1} \left (t \right )+x_{2} \left (t \right )+1 \\
x_{2}^{\prime }\left (t \right )&=6 x_{1} \left (t \right )-5 x_{2} \left (t \right )+{\mathrm e}^{-t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 26 |
\begin{align*}
x_{1}^{\prime }\left (t \right )&=9 x_{1} \left (t \right )-2 x_{2} \left (t \right )+9 t \\
x_{2}^{\prime }\left (t \right )&=5 x_{1} \left (t \right )-2 x_{2} \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 27 |
\begin{align*}
x_{1}^{\prime }\left (t \right )&=10 x_{1} \left (t \right )-4 x_{2} \left (t \right ) \\
x_{2}^{\prime }\left (t \right )&=4 x_{1} \left (t \right )+2 x_{2} \left (t \right )+\frac {{\mathrm e}^{6 t}}{t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 28 |
\begin{align*}
x_{1}^{\prime }\left (t \right )&=2 x_{1} \left (t \right )-4 x_{2} \left (t \right )+3 x_{3} \left (t \right )+{\mathrm e}^{6 t} \\
x_{2}^{\prime }\left (t \right )&=-9 x_{1} \left (t \right )-3 x_{2} \left (t \right )-9 x_{3} \left (t \right )+1 \\
x_{3}^{\prime }\left (t \right )&=4 x_{1} \left (t \right )+4 x_{2} \left (t \right )+3 x_{3} \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 29 |
\begin{align*}
x_{1}^{\prime }\left (t \right )&=2 x_{1} \left (t \right )-2 x_{2} \left (t \right )+x_{3} \left (t \right )+t \\
x_{2}^{\prime }\left (t \right )&=x_{1} \left (t \right )-4 x_{2} \left (t \right )+x_{3} \left (t \right ) \\
x_{3}^{\prime }\left (t \right )&=2 x_{1} \left (t \right )+2 x_{2} \left (t \right )-3 x_{3} \left (t \right )+1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 34 |
\begin{align*}
x_{1}^{\prime }\left (t \right )&=-3 x_{1} \left (t \right )+4 x_{2} \left (t \right ) \\
x_{2}^{\prime }\left (t \right )&=8 x_{1} \left (t \right )+x_{2} \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 35 |
\begin{align*}
x_{1}^{\prime }\left (t \right )&=-6 x_{2} \left (t \right ) \\
x_{2}^{\prime }\left (t \right )&=x_{1} \left (t \right )-5 x_{2} \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 36 |
\begin{align*}
x_{1}^{\prime }\left (t \right )&=5 x_{1} \left (t \right )+9 x_{2} \left (t \right ) \\
x_{2}^{\prime }\left (t \right )&=-2 x_{1} \left (t \right )-x_{2} \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 37 |
\begin{align*}
x_{1}^{\prime }\left (t \right )&=-4 x_{1} \left (t \right ) \\
x_{2}^{\prime }\left (t \right )&=-4 x_{2} \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 38 |
\begin{align*}
x_{1}^{\prime }\left (t \right )&=7 x_{1} \left (t \right )-2 x_{2} \left (t \right ) \\
x_{2}^{\prime }\left (t \right )&=x_{1} \left (t \right )+4 x_{2} \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 39 |
\begin{align*}
x_{1}^{\prime }\left (t \right )&=-3 x_{1} \left (t \right )-5 x_{2} \left (t \right ) \\
x_{2}^{\prime }\left (t \right )&=x_{1} \left (t \right )-7 x_{2} \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 40 |
\begin{align*}
x_{1}^{\prime }\left (t \right )&=-2 x_{1} \left (t \right )-x_{2} \left (t \right ) \\
x_{2}^{\prime }\left (t \right )&=x_{1} \left (t \right )-4 x_{2} \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 41 | \begin{align*}
x_{1}^{\prime }\left (t \right )&=10 x_{1} \left (t \right )-8 x_{2} \left (t \right ) \\
x_{2}^{\prime }\left (t \right )&=2 x_{1} \left (t \right )+2 x_{2} \left (t \right ) \\
\end{align*} | ✓ | ✓ | ✓ | ✓ |
|
| ID | problem | ODE | Solved? | Maple | Mma | Sympy |
| Problem 1 |
\begin{align*}
-2 y+y^{\prime }&=6 \,{\mathrm e}^{5 t} \\
y \left (0\right ) &= 3 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
|
| Problem 2 |
\begin{align*}
y+y^{\prime }&=8 \,{\mathrm e}^{3 t} \\
y \left (0\right ) &= 2 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
|
| Problem 3 |
\begin{align*}
3 y+y^{\prime }&=2 \,{\mathrm e}^{-t} \\
y \left (0\right ) &= 3 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
|
| Problem 4 |
\begin{align*}
y^{\prime }+2 y&=4 t \\
y \left (0\right ) &= 1 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
|
| Problem 5 |
\begin{align*}
-y+y^{\prime }&=6 \cos \left (t \right ) \\
y \left (0\right ) &= 2 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
|
| Problem 6 |
\begin{align*}
-y+y^{\prime }&=5 \sin \left (2 t \right ) \\
y \left (0\right ) &= -1 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
|
| Problem 7 |
\begin{align*}
y+y^{\prime }&=5 \,{\mathrm e}^{t} \sin \left (t \right ) \\
y \left (0\right ) &= 1 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
|
| Problem 8 |
\begin{align*}
y^{\prime \prime }+y^{\prime }-2 y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 4 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
|
| Problem 9 |
\begin{align*}
y^{\prime \prime }+4 y&=0 \\
y \left (0\right ) &= 5 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
|
| Problem 10 |
\begin{align*}
y^{\prime \prime }-3 y^{\prime }+2 y&=4 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
|
| Problem 11 |
\begin{align*}
y^{\prime \prime }-y^{\prime }-12 y&=36 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 12 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
|
| Problem 12 |
\begin{align*}
y^{\prime \prime }+y^{\prime }-2 y&=10 \,{\mathrm e}^{-t} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
|
| Problem 13 |
\begin{align*}
y^{\prime \prime }-3 y^{\prime }+2 y&=4 \,{\mathrm e}^{3 t} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
|
| Problem 14 |
\begin{align*}
y^{\prime \prime }-2 y^{\prime }&=30 \,{\mathrm e}^{-3 t} \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
|
| Problem 15 |
\begin{align*}
y^{\prime \prime }-y&=12 \,{\mathrm e}^{2 t} \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
|
| Problem 16 |
\begin{align*}
y^{\prime \prime }+4 y&=10 \,{\mathrm e}^{-t} \\
y \left (0\right ) &= 4 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
|
| Problem 17 |
\begin{align*}
y^{\prime \prime }-y^{\prime }-6 y&=12-6 \,{\mathrm e}^{t} \\
y \left (0\right ) &= 5 \\
y^{\prime }\left (0\right ) &= -3 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
|
| Problem 18 | \begin{align*}
y^{\prime \prime }-y&=6 \cos \left (t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 4 \\
\end{align*} Using Laplace transform method. | ✓ | ✓ | ✓ | ✓ |
|
| Problem 19 |
\begin{align*}
y^{\prime \prime }-9 y&=13 \sin \left (2 t \right ) \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
|
| Problem 20 |
\begin{align*}
y^{\prime \prime }-y&=8 \sin \left (t \right )-6 \cos \left (t \right ) \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
|
| Problem 21 |
\begin{align*}
y^{\prime \prime }-y^{\prime }-2 y&=10 \cos \left (t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
|
| Problem 22 |
\begin{align*}
y^{\prime \prime }+5 y^{\prime }+4 y&=20 \sin \left (2 t \right ) \\
y \left (0\right ) &= -1 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
|
| Problem 23 |
\begin{align*}
y^{\prime \prime }+5 y^{\prime }+4 y&=20 \sin \left (2 t \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -2 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
|
| Problem 24 |
\begin{align*}
y^{\prime \prime }-3 y^{\prime }+2 y&=3 \cos \left (t \right )+\sin \left (t \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
|
| Problem 25 |
\begin{align*}
y^{\prime \prime }+4 y&=9 \sin \left (t \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
|
| Problem 26 |
\begin{align*}
y^{\prime \prime }+y&=6 \cos \left (2 t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
|
| Problem 27 |
\begin{align*}
y^{\prime \prime }+9 y&=7 \sin \left (4 t \right )+14 \cos \left (4 t \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
|
| Problem 28 |
\begin{align*}
y^{\prime \prime }-y&=0 \\
y \left (0\right ) &= A \\
y^{\prime }\left (0\right ) &= B \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
|
| ID | problem | ODE | Solved? | Maple | Mma | Sympy |
| Problem 27 |
\begin{align*}
y^{\prime }+2 y&=2 \operatorname {Heaviside}\left (t -1\right ) \\
y \left (0\right ) &= 1 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
|
| Problem 28 |
\begin{align*}
-2 y+y^{\prime }&=\operatorname {Heaviside}\left (t -2\right ) {\mathrm e}^{t -2} \\
y \left (0\right ) &= 2 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
|
| Problem 29 |
\begin{align*}
-y+y^{\prime }&=4 \operatorname {Heaviside}\left (t -\frac {\pi }{4}\right ) \sin \left (t +\frac {\pi }{4}\right ) \\
y \left (0\right ) &= 1 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
|
| Problem 30 |
\begin{align*}
y^{\prime }+2 y&=\operatorname {Heaviside}\left (t -\pi \right ) \sin \left (2 t \right ) \\
y \left (0\right ) &= 3 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
|
| Problem 31 |
\begin{align*}
3 y+y^{\prime }&=\left \{\begin {array}{cc} 1 & 0\le t <1 \\ 0 & 1\le t \end {array}\right . \\
y \left (0\right ) &= 1 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
|
| Problem 32 |
\begin{align*}
y^{\prime }-3 y&=\left \{\begin {array}{cc} \sin \left (t \right ) & 0\le t <\frac {\pi }{2} \\ 1 & \frac {\pi }{2}\le t \end {array}\right . \\
y \left (0\right ) &= 2 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
|
| Problem 33 |
\begin{align*}
y^{\prime }-3 y&=-10 \,{\mathrm e}^{-t +a} \sin \left (-2 t +2 a \right ) \operatorname {Heaviside}\left (t -a \right ) \\
y \left (0\right ) &= 5 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
|
| Problem 34 |
\begin{align*}
y^{\prime \prime }-y&=\operatorname {Heaviside}\left (t -1\right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
|
| Problem 35 |
\begin{align*}
y^{\prime \prime }-y^{\prime }-2 y&=1-3 \operatorname {Heaviside}\left (t -2\right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -2 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
|
| Problem 36 |
\begin{align*}
y^{\prime \prime }-4 y&=\operatorname {Heaviside}\left (t -1\right )-\operatorname {Heaviside}\left (t -2\right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 4 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
|
| Problem 37 |
\begin{align*}
y^{\prime \prime }+y&=t -\operatorname {Heaviside}\left (t -1\right ) \left (t -1\right ) \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
|
| Problem 38 |
\begin{align*}
y^{\prime \prime }+3 y^{\prime }+2 y&=-10 \operatorname {Heaviside}\left (t -\frac {\pi }{4}\right ) \cos \left (t +\frac {\pi }{4}\right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
|
| Problem 39 |
\begin{align*}
y^{\prime \prime }+y^{\prime }-6 y&=30 \operatorname {Heaviside}\left (t -1\right ) {\mathrm e}^{1-t} \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= -4 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
|
| Problem 40 |
\begin{align*}
y^{\prime \prime }+4 y^{\prime }+5 y&=5 \operatorname {Heaviside}\left (-3+t \right ) \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
|
| Problem 41 |
\begin{align*}
y^{\prime \prime }-2 y^{\prime }+5 y&=2 \sin \left (t \right )+\operatorname {Heaviside}\left (t -\frac {\pi }{2}\right ) \left (1+\cos \left (t \right )\right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
|
| Problem 46 part a |
\begin{align*}
-y+y^{\prime }&=\left \{\begin {array}{cc} 2 & 0\le t <1 \\ -1 & 1\le t \end {array}\right . \\
y \left (0\right ) &= 1 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
|
| Problem 46 part b |
\begin{align*}
-y+y^{\prime }&=\left \{\begin {array}{cc} 2 & 0\le t <1 \\ -1 & 1\le t \end {array}\right . \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| ID | problem | ODE | Solved? | Maple | Mma | Sympy |
| Problem 1 |
\begin{align*}
y+y^{\prime }&=\delta \left (t -5\right ) \\
y \left (0\right ) &= 3 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
|
| Problem 2 |
\begin{align*}
-2 y+y^{\prime }&=\delta \left (t -2\right ) \\
y \left (0\right ) &= 1 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
|
| Problem 3 |
\begin{align*}
y^{\prime }+4 y&=3 \delta \left (t -1\right ) \\
y \left (0\right ) &= 2 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
|
| Problem 4 |
\begin{align*}
y^{\prime }-5 y&=2 \,{\mathrm e}^{-t}+\delta \left (-3+t \right ) \\
y \left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
|
| Problem 5 |
\begin{align*}
y^{\prime \prime }-3 y^{\prime }+2 y&=\delta \left (t -1\right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
|
| Problem 6 |
\begin{align*}
y^{\prime \prime }-4 y&=\delta \left (-3+t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
|
| Problem 7 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }+5 y&=\delta \left (t -\frac {\pi }{2}\right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
|
| Problem 8 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime }+13 y&=\delta \left (t -\frac {\pi }{4}\right ) \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
|
| Problem 9 |
\begin{align*}
y^{\prime \prime }+4 y^{\prime }+3 y&=\delta \left (t -2\right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
|
| Problem 10 |
\begin{align*}
y^{\prime \prime }+6 y^{\prime }+13 y&=\delta \left (t -\frac {\pi }{4}\right ) \\
y \left (0\right ) &= 5 \\
y^{\prime }\left (0\right ) &= 5 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
|
| Problem 11 |
\begin{align*}
y^{\prime \prime }+9 y&=15 \sin \left (2 t \right )+\delta \left (t -\frac {\pi }{6}\right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
|
| Problem 12 |
\begin{align*}
y^{\prime \prime }+16 y&=4 \cos \left (3 t \right )+\delta \left (t -\frac {\pi }{3}\right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
|
| Problem 13 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }+5 y&=4 \sin \left (t \right )+\delta \left (t -\frac {\pi }{6}\right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
|
| ID | problem | ODE | Solved? | Maple | Mma | Sympy |
| Problem 1 |
\begin{align*}
y^{\prime \prime }-y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
|
| Problem 2 |
\begin{align*}
y^{\prime \prime }+2 x y^{\prime }+4 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
|
| Problem 3 |
\begin{align*}
y^{\prime \prime }-2 x y^{\prime }-2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
|
| Problem 4 |
\begin{align*}
y^{\prime \prime }-x^{2} y^{\prime }-2 y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
|
| Problem 5 |
\begin{align*}
y^{\prime \prime }+y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
|
| Problem 6 |
\begin{align*}
y^{\prime \prime }+x y^{\prime }+3 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
|
| Problem 7 |
\begin{align*}
y^{\prime \prime }-x^{2} y^{\prime }-3 y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
|
| Problem 8 |
\begin{align*}
y^{\prime \prime }+2 x^{2} y^{\prime }+2 y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
|
| Problem 9 |
\begin{align*}
\left (x^{2}-3\right ) y^{\prime \prime }-3 x y^{\prime }-5 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
|
| Problem 10 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }+4 x y^{\prime }+2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
|
| Problem 11 |
\begin{align*}
\left (-4 x^{2}+1\right ) y^{\prime \prime }-20 x y^{\prime }-16 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
|
| Problem 12 |
\begin{align*}
\left (x^{2}-1\right ) y^{\prime \prime }-6 x y^{\prime }+12 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
|
| Problem 13 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }+4 y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
|
| Problem 14 |
\begin{align*}
y^{\prime \prime }+x y^{\prime }+\left (x +2\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
|
| Problem 15 |
\begin{align*}
y^{\prime \prime }-y \,{\mathrm e}^{x}&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
|
| Problem 17 |
\begin{align*}
x y^{\prime \prime }-\left (x -1\right ) y^{\prime }-y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
|
| Problem 18 |
\begin{align*}
\left (2 x^{2}+1\right ) y^{\prime \prime }+7 x y^{\prime }+2 y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
|
| Problem 19 | \begin{align*}
4 y^{\prime \prime }+x y^{\prime }+4 y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Series expansion around \(x=0\). | ✓ | ✓ | ✓ | ✓ |
|
| Problem 20 |
\begin{align*}
y^{\prime \prime }+2 x^{2} y^{\prime }+y x&=2 \cos \left (x \right ) \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
|
| Problem 21 |
\begin{align*}
y^{\prime \prime }+x y^{\prime }-4 y&=6 \,{\mathrm e}^{x} \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
|
| ID | problem | ODE | Solved? | Maple | Mma | Sympy |
| 1 |
\begin{align*}
y^{\prime \prime }+\frac {y^{\prime }}{1-x}+y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
|
| 3 |
\begin{align*}
x^{2} y^{\prime \prime }+\frac {x y^{\prime }}{\left (-x^{2}+1\right )^{2}}+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
|
| 4 |
\begin{align*}
\left (x -2\right )^{2} y^{\prime \prime }+\left (x -2\right ) {\mathrm e}^{x} y^{\prime }+\frac {4 y}{x}&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
|
| 5 |
\begin{align*}
y^{\prime \prime }+\frac {2 y^{\prime }}{x \left (x -3\right )}-\frac {y}{x^{3} \left (x +3\right )}&=0 \\
\end{align*} Series expansion around \(x=0\). |
✗ |
✗ |
✓ |
✗ |
|
| 6 |
\begin{align*}
x^{2} y^{\prime \prime }+x \left (1-x \right ) y^{\prime }-7 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
|
| 7 |
\begin{align*}
4 x^{2} y^{\prime \prime }+{\mathrm e}^{x} y^{\prime } x -y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
|
| 8 |
\begin{align*}
4 x y^{\prime \prime }-x y^{\prime }+2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
|
| 9 |
\begin{align*}
x^{2} y^{\prime \prime }-x \cos \left (x \right ) y^{\prime }+5 y \,{\mathrm e}^{2 x}&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
|
| 10 |
\begin{align*}
4 x^{2} y^{\prime \prime }+3 x y^{\prime }+y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
|
| 11 |
\begin{align*}
6 x^{2} y^{\prime \prime }+x \left (1+18 x \right ) y^{\prime }+\left (1+12 x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
|
| 12 |
\begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }-\left (x +2\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
|
| 13 |
\begin{align*}
2 x y^{\prime \prime }+y^{\prime }-2 y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
|
| 14 |
\begin{align*}
3 x^{2} y^{\prime \prime }-x \left (8+x \right ) y^{\prime }+6 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
|
| 15 |
\begin{align*}
2 x^{2} y^{\prime \prime }-x \left (2 x +1\right ) y^{\prime }+2 \left (4 x -1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
|
| 16 |
\begin{align*}
x^{2} y^{\prime \prime }+x \left (1-x \right ) y^{\prime }-\left (5+x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
|
| 17 |
\begin{align*}
3 x^{2} y^{\prime \prime }+x \left (7+3 x \right ) y^{\prime }+\left (1+6 x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
|
| 18 |
\begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }+\left (1-x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
|
| 19 | \begin{align*}
3 x^{2} y^{\prime \prime }+x \left (3 x^{2}+1\right ) y^{\prime }-2 y x&=0 \\
\end{align*} Series expansion around \(x=0\). | ✓ | ✓ | ✓ | ✓ |
|
| 20 |
\begin{align*}
4 x^{2} y^{\prime \prime }-4 x^{2} y^{\prime }+\left (2 x +1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
|
| 21 |
\begin{align*}
x^{2} y^{\prime \prime }+x \left (3-2 x \right ) y^{\prime }+\left (1-2 x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
|
| ID | problem | ODE | Solved? | Maple | Mma | Sympy |
| Example 11.5.2 page 763 |
\begin{align*}
x^{2} y^{\prime \prime }-x \left (x +3\right ) y^{\prime }+\left (4-x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
|
| Example 11.5.4 page 765 |
\begin{align*}
x^{2} y^{\prime \prime }+x \left (-x +3\right ) y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
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|
| Example 11.5.5 page 768 |
\begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }-\left (x +4\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
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|
| (a) |
\begin{align*}
x^{2} y^{\prime \prime }-\left (-x^{2}+x \right ) y^{\prime }+\left (x^{3}+1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
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|
| (b) |
\begin{align*}
x^{2} y^{\prime \prime }-\left (2 \sqrt {5}-1\right ) x y^{\prime }+\left (\frac {19}{4}-3 x^{2}\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
|
| (c) |
\begin{align*}
x^{2} y^{\prime \prime }+\left (-2 x^{5}+9 x \right ) y^{\prime }+\left (10 x^{4}+5 x^{2}+25\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
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✗ |
|
| (d) |
\begin{align*}
x^{2} y^{\prime \prime }+\left (4 x +\frac {1}{2} x^{2}-\frac {1}{3} x^{3}\right ) y^{\prime }-\frac {7 y}{4}&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
|
| (e) |
\begin{align*}
x^{2} y^{\prime \prime }+x^{2} y^{\prime }+y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
|
| 1 |
\begin{align*}
x^{2} y^{\prime \prime }+x \left (x -3\right ) y^{\prime }+\left (4-x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
|
| 2 |
\begin{align*}
4 x^{2} y^{\prime \prime }+2 x^{2} y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
|
| 3 |
\begin{align*}
x^{2} y^{\prime \prime }+x \cos \left (x \right ) y^{\prime }-2 y \,{\mathrm e}^{x}&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
|
| 4 |
\begin{align*}
x^{2} y^{\prime \prime }+x^{2} y^{\prime }-\left (x +2\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
|
| 5 |
\begin{align*}
x^{2} y^{\prime \prime }+2 x^{2} y^{\prime }+\left (x -\frac {3}{4}\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
|
| 6 |
\begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }+\left (2 x -1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
|
| 7 |
\begin{align*}
x^{2} y^{\prime \prime }+x^{3} y^{\prime }-\left (x +2\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
|
| 8 |
\begin{align*}
x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+7 \,{\mathrm e}^{x} y^{\prime } x +9 \left (1+\tan \left (x \right )\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
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| 11 | \begin{align*}
x^{2} \left (x +1\right ) y^{\prime \prime }+x^{2} y^{\prime }-2 y&=0 \\
\end{align*} Series expansion around \(x=0\). | ✓ | ✓ | ✓ | ✓ |
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| 12 |
\begin{align*}
x^{2} y^{\prime \prime }+3 x y^{\prime }+\left (1-x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
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✓ |
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| 13 |
\begin{align*}
x y^{\prime \prime }-y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
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|
| 14 |
\begin{align*}
x^{2} y^{\prime \prime }+x \left (x^{2}+6\right ) y^{\prime }+6 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
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|
| 15 |
\begin{align*}
x^{2} y^{\prime \prime }+x \left (1-x \right ) y^{\prime }-y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
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| 16 |
\begin{align*}
4 x^{2} y^{\prime \prime }+\left (1-4 x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
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✓ |
|
| 17 |
\begin{align*}
x y^{\prime \prime }+y^{\prime }-2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
|
| 18 |
\begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }-\left (x +1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
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✓ |
|
| 19 |
\begin{align*}
x^{2} y^{\prime \prime }-x \left (x +3\right ) y^{\prime }+4 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
|
| 20 |
\begin{align*}
x^{2} y^{\prime \prime }-x^{2} y^{\prime }-2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
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|
| 21 |
\begin{align*}
x^{2} y^{\prime \prime }-x^{2} y^{\prime }-\left (3 x +2\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
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|
| 22 |
\begin{align*}
x^{2} y^{\prime \prime }+x \left (5-x \right ) y^{\prime }+4 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
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| 23 |
\begin{align*}
4 x^{2} y^{\prime \prime }+4 x \left (1-x \right ) y^{\prime }+\left (2 x -9\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
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|
| 24 |
\begin{align*}
x^{2} y^{\prime \prime }+2 x \left (x +2\right ) y^{\prime }+2 \left (x +1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
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|
| 25 |
\begin{align*}
x^{2} y^{\prime \prime }-x \left (1-x \right ) y^{\prime }+\left (1-x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
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|
| 26 |
\begin{align*}
4 x^{2} y^{\prime \prime }+4 x \left (2 x +1\right ) y^{\prime }+\left (4 x -1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
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|
| 27 |
\begin{align*}
4 x^{2} y^{\prime \prime }-\left (4 x +3\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
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|
| 28 |
\begin{align*}
x y^{\prime \prime }-x y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
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|
| 29 |
\begin{align*}
x^{2} y^{\prime \prime }+x \left (x +4\right ) y^{\prime }+\left (x +2\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
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|
| ID | problem | ODE | Solved? | Maple | Mma | Sympy |
| 2 |
\begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {9}{4}\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
|
| 3 |
\begin{align*}
x y^{\prime \prime }-y^{\prime }+y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
|
| ID | problem | ODE | Solved? | Maple | Mma | Sympy |
| 1 |
\begin{align*}
y^{\prime \prime }+y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
|
| 2 |
\begin{align*}
y^{\prime \prime }-x^{2} y&=0 \\
\end{align*} Series expansion around \(x=0\). |
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✓ |
|
| 3 |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }-6 x y^{\prime }-4 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
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|
| 4 |
\begin{align*}
x y^{\prime \prime }+y^{\prime }+2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
|
| 5 |
\begin{align*}
x y^{\prime \prime }+2 y^{\prime }+y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
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✓ |
|
| 6 |
\begin{align*}
2 x y^{\prime \prime }+5 \left (1-2 x \right ) y^{\prime }-5 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
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|
| 7 |
\begin{align*}
x y^{\prime \prime }+y^{\prime }+y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
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✓ |
|
| 8 |
\begin{align*}
\left (4 x^{2}+1\right ) y^{\prime \prime }-8 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
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|
| 9 |
\begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
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|
| 10 |
\begin{align*}
4 x y^{\prime \prime }+3 y^{\prime }+3 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
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|
| 11 |
\begin{align*}
x^{2} y^{\prime \prime }+\frac {3 x y^{\prime }}{2}-\frac {\left (x +1\right ) y}{2}&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
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✓ |
|
| 12 |
\begin{align*}
x^{2} y^{\prime \prime }-x \left (2-x \right ) y^{\prime }+\left (x^{2}+2\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
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✓ |
|
| 13 |
\begin{align*}
x^{2} y^{\prime \prime }-3 x y^{\prime }+4 \left (x +1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
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|
| 20 |
\begin{align*}
y^{\prime \prime }+\left (1-\frac {3}{4 x^{2}}\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
|