| # | ODE | Mathematica | Maple | Sympy |
| \[
{} y y^{\prime }+a \left (2 b x +1\right ) {\mathrm e}^{b x} y = -a^{2} b \,x^{2} {\mathrm e}^{2 b x}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y y^{\prime }-a \left (1+2 n +2 n \left (n +1\right ) x \right ) {\mathrm e}^{\left (n +1\right ) x} y = -a^{2} n \left (n +1\right ) \left (n x +1\right ) x \,{\mathrm e}^{2 \left (n +1\right ) x}
\]
|
✗ |
✓ |
✗ |
|
| \[
{} y y^{\prime }+a \left (1+2 b \sqrt {x}\right ) {\mathrm e}^{2 b \sqrt {x}} y = -a^{2} b \,x^{{3}/{2}} {\mathrm e}^{4 b \sqrt {x}}
\]
|
✗ |
✓ |
✗ |
|
| \[
{} y y^{\prime } = \left (a \cosh \left (x \right )+b \right ) y-a b \sinh \left (x \right )+c
\]
|
✗ |
✗ |
✗ |
|
| \[
{} y y^{\prime } = \left (a \sinh \left (x \right )+b \right ) y-a b \cosh \left (x \right )+c
\]
|
✗ |
✗ |
✗ |
|
| \[
{} y y^{\prime } = \left (2 \ln \left (x \right )+a +1\right ) y+x \left (-\ln \left (x \right )^{2}-a \ln \left (x \right )+b \right )
\]
|
✗ |
✓ |
✗ |
|
| \[
{} y y^{\prime } = \left (2 \ln \left (x \right )^{2}+2 \ln \left (x \right )+a \right ) y+x \left (-\ln \left (x \right )^{4}-a \ln \left (x \right )^{2}+b \right )
\]
|
✗ |
✗ |
✗ |
|
| \[
{} y y^{\prime } = a x \cos \left (\lambda \,x^{2}\right ) y+x
\]
|
✗ |
✗ |
✗ |
|
| \[
{} y y^{\prime } = a x \sin \left (\lambda \,x^{2}\right ) y+x
\]
|
✗ |
✗ |
✗ |
|
| \[
{} \left (A y+B x +a \right ) y^{\prime }+B y+k x +b = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (y+a x +b \right ) y^{\prime } = \alpha y+\beta x +\gamma
\]
|
✗ |
✓ |
✗ |
|
| \[
{} \left (y+a k \,x^{2}+b x +c \right ) y^{\prime } = -a y^{2}+2 a k x y+m y+k \left (k +b -m \right ) x +s
\]
|
✗ |
✗ |
✗ |
|
| \[
{} \left (y+A \,x^{n}+a \right ) y^{\prime }+n A \,x^{n -1} y+k \,x^{m}+b = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (y+a \,x^{n +1}+b \,x^{n}\right ) y^{\prime } = \left (a n \,x^{n}+c \,x^{n -1}\right ) y
\]
|
✗ |
✗ |
✗ |
|
| \[
{} y y^{\prime } x = a y^{2}+b y+c \,x^{n}+s
\]
|
✗ |
✗ |
✗ |
|
| \[
{} y y^{\prime } x = -n y^{2}+a \left (2 n +1\right ) x y+b y-a^{2} n \,x^{2}-a b x +c
\]
|
✗ |
✓ |
✗ |
|
| \[
{} 2 y y^{\prime } x = \left (-n +1\right ) y^{2}+\left (a \left (2 n +1\right ) x +2 n -1\right ) y-a^{2} n \,x^{2}-b x -n
\]
|
✗ |
✓ |
✗ |
|
| \[
{} \left (a x y-a k y+b x -b k \right ) y^{\prime } = c y^{2}+d x y+\left (-d k +b \right ) y
\]
|
✗ |
✓ |
✗ |
|
| \[
{} \left (\left (3 a x +\lambda s \right ) y+\left (3 s +4 \lambda \right ) x \right ) y^{\prime } = 2 a y^{2}+6 \lambda +2 s +2 x
\]
|
✗ |
✗ |
✗ |
|
| \[
{} \left (\left (4 a x +\lambda s \right ) y+\left (3 s +4 \lambda \right ) x \right ) y^{\prime } = \frac {3 a y^{2}}{2}+6 \lambda +2 s +2 x
\]
|
✗ |
✗ |
✗ |
|
| \[
{} \left (2 A x y+a y+b x +c \right ) y^{\prime } = A y^{2}+A \,k^{2} x^{2}+m y+k \left (a k +b -m \right ) x +s
\]
|
✗ |
✗ |
✗ |
|
| \[
{} \left (2 x y+\left (1-m \right ) A y-\frac {2 \left (1+m \right ) x}{3+m}\right ) y^{\prime } = \frac {\left (1-m \right ) y^{2}}{2}+\frac {\left (m -1\right ) y}{3+m}+x
\]
|
✗ |
✗ |
✗ |
|
| \[
{} x \left (2 a y+b x \right ) y^{\prime } = a \left (2-m \right ) y^{2}+b \left (1-m \right ) x y+c \,x^{2}+A \,x^{m +2}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (x y+x^{2}+a \right ) y^{\prime } = y^{2}+x y+b
\]
|
✓ |
✓ |
✓ |
|
| \[
{} \left (2 A x y+B \,x^{2}+b \right ) y^{\prime } = A y^{2}+k \left (A k +B \right ) x^{2}+c
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (A x y+B \,x^{2}+k x \right ) y^{\prime } = d y^{2}+e x y+f \,x^{2}+k y
\]
|
✗ |
✗ |
✗ |
|
| \[
{} \left (A x y+B \,x^{2}+k x \right ) y^{\prime } = A y^{2}+B x y+\left (A b +k \right ) y+B b x +b k
\]
|
✓ |
✓ |
✓ |
|
| \[
{} \left (2 A x y+B \,x^{2}+k x \right ) y^{\prime } = A y^{2}+c x y+d \,x^{2}-c \beta x -A \,\beta ^{2}-k \beta
\]
|
✗ |
✗ |
✗ |
|
| \[
{} \left (A x y+B \,x^{2}+k x \right ) y^{\prime } = A y^{2}+c x y+d \,x^{2}+\left (-A \beta +k \right ) y-c \beta x -k \beta
\]
|
✗ |
✓ |
✗ |
|
| \[
{} \left (A x y+A k y+B \,x^{2}+B k x \right ) y^{\prime } = c y^{2}+d x y+k \left (d -B \right ) y
\]
|
✗ |
✓ |
✗ |
|
| \[
{} \left (A x y+B \,x^{2}+a_{1} x +b_{1} y+c_{1} \right ) y^{\prime } = A y^{2}+B x y+a_{2} x +b_{2} y+c_{2}
\]
|
✗ |
✓ |
✗ |
|
| \[
{} \left (A x y+B \,x^{2}+a y+b x +c \right ) y^{\prime } = k A x y+k B \,x^{2}+m y+k \left (a k +b -m \right ) x +s
\]
|
✗ |
✗ |
✗ |
|
| \[
{} \left (2 A x y+B \,x^{2}+a y+b x +c \right ) y^{\prime } = A y^{2}+k \left (A k +B \right ) x^{2}+a k y+b k x +s
\]
|
✗ |
✗ |
✗ |
|
| \[
{} \left (2 A x y-A k \,x^{2}+a y+b x +c \right ) y^{\prime } = A y^{2}+m y+k \left (a k +b -m \right ) x +s
\]
|
✗ |
✗ |
✗ |
|
| \[
{} \left (2 A x y+B \,x^{2}+a y-a k x +b \right ) y^{\prime } = A y^{2}+k \left (A k +B \right ) x^{2}+m y-m k x +s
\]
|
✗ |
✗ |
✗ |
|
| \[
{} \left (2 A x y+B \,x^{2}+a y+b x +c \right ) y^{\prime } = A y^{2}+k \left (A k +B \right ) x^{2}+b y+a \,k^{2} x +s
\]
|
✗ |
✗ |
✗ |
|
| \[
{} \left (A x y+B \,x^{2}+\left (k -1\right ) A a y-\left (A b k +B a \right ) x \right ) y^{\prime } = A y^{2}+B x y-\left (B a k +A b \right ) y+\left (k -1\right ) B b x
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (\left (a x +c \right ) y+\left (-n +1\right ) x^{2}+\left (-1+2 n \right ) x -n \right ) y^{\prime } = 2 a y^{2}+2 x y
\]
|
✗ |
✓ |
✗ |
|
| \[
{} \left (\left (x +c \right ) y+\left (n +1\right ) x^{2}-a \left (2 n +1\right ) x +a^{2} n \right ) y^{\prime } = \frac {2 n y^{2}}{3 n -1}+2 x y
\]
|
✗ |
✗ |
✗ |
|
| \[
{} x \left (2 a x y+b \right ) y^{\prime } = -a \left (3+m \right ) x y^{2}-b \left (m +2\right ) y+c \,x^{m}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (\left (a_{2} x^{2}+a_{1} x +a_{0} \right ) y+b_{2} x^{2}+b_{1} x +b_{0} \right ) y^{\prime } = c_{2} y^{2}+c_{1} y+c_{0}
\]
|
✗ |
✗ |
✗ |
|
| \[
{} \left (\left (12 a^{2} x^{2}-7 a x +1\right ) y+4 c \,x^{2}-5 b x \right ) y^{\prime } = -2 x \left (3 a^{2} y^{2}+2 c y+3 b^{2}\right )
\]
|
✗ |
✗ |
✗ |
|
| \[
{} x \left (\left (m -1\right ) \left (A x +B \right ) y+m \left (d \,x^{2}+e x +F \right )\right ) y^{\prime } = \left (A \left (-n +1\right ) x -B n \right ) y^{2}+\left (d \left (-n +2\right ) x^{2}+e \left (-n +1\right ) x -F n \right ) y
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x \left (2 a x y+b \right ) y^{\prime } = -4 a \,x^{2} y^{2}-3 b x y+c \,x^{2}+k
\]
|
✗ |
✗ |
✗ |
|
| \[
{} \left (x y+a \,x^{n}+b \,x^{2}\right ) y^{\prime } = y^{2}+c \,x^{n}+b x y
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x \left (2 a \,x^{n} y+b \right ) y^{\prime } = -a \left (3 n +m \right ) x^{n} y^{2}-b \left (2 n +m \right ) y+A \,x^{m}+x \,x^{-n}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y y^{\prime } = -n y^{2}+a \left (2 n +1\right ) {\mathrm e}^{x} y+b y-a^{2} n \,{\mathrm e}^{2 x}-a b \,{\mathrm e}^{x}+c
\]
|
✗ |
✗ |
✗ |
|
| \[
{} y^{\prime } = a y^{3}+\frac {b}{x^{{3}/{2}}}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime } = -y^{3}+3 a^{2} x^{2} y-2 a^{3} x^{3}+a
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime } = -y^{3}+\left (a x +b \right ) y^{2}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime } = -y^{3}+\frac {y^{2}}{\left (a x +b \right )^{2}}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime } = -y^{3}+\frac {y^{2}}{\sqrt {a x +b}}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime } = a y^{3}+3 a b x y^{2}-b -2 a \,b^{3} x^{3}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime } = a x y^{3}+b y^{2}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime } = a x y^{3}+2 a b \,x^{2} y^{2}-b -2 a \,b^{3} x^{4}
\]
|
✗ |
✗ |
✗ |
|
| \[
{} y^{\prime } = a \,x^{2 n +1} y^{3}+b \,x^{-n -2}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime } = a \,x^{n} y^{3}+3 a b \,x^{m +n} y^{2}-b m \,x^{m -1}-2 a \,b^{3} x^{n +3 m}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime } = a \,x^{n} y^{3}+3 a b \,x^{m +n} y^{2}+c \,x^{k} y-2 a \,b^{3} x^{n +3 m}+b c \,x^{m +k}-b m \,x^{m -1}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} 9 y^{\prime } = -x^{m} \left (a \,x^{1-m}+b \right )^{2 \lambda +1} y^{3}-x^{-2 m} \left (9 a +2+9 b m \,x^{m -1}\right ) \left (a \,x^{1-m}+b \right )^{-\lambda -2}
\]
|
✗ |
✗ |
✗ |
|
| \[
{} x y^{\prime } = a \,x^{4} y^{3}+\left (b \,x^{2}-1\right ) y+c x
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x y^{\prime } = a y^{3}+3 a b \,x^{n} y^{2}-b n \,x^{n}-2 a \,b^{3} x^{3 n}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x y^{\prime } = 3 x^{2 n +1} y^{3}+\left (b x -n \right ) y+c \,x^{-n +1}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x y^{\prime } = a \,x^{n +2} y^{3}+\left (b \,x^{n}-1\right ) y+c \,x^{n -1}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x^{2} y^{\prime } = y^{3}-3 y a^{2} x^{4}+2 a^{3} x^{6}+2 a \,x^{3}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime } = -\left (a x +b \,x^{m}\right ) y^{3}+y^{2}
\]
|
✗ |
✗ |
✗ |
|
| \[
{} y^{\prime } = \frac {y^{3}}{\sqrt {x^{2} a +b x +c}}+y^{2}
\]
|
✗ |
✗ |
✗ |
|
| \[
{} y^{\prime } = -\frac {\left (a x -\frac {6}{25}\right )^{{34}/{9}} y^{3}}{x^{{16}/{9}}}+\frac {\frac {2 a x}{3}-\frac {4}{675}}{x^{{11}/{18}} \left (a x -\frac {6}{25}\right )^{{61}/{18}}}
\]
|
✓ |
✗ |
✗ |
|
| \[
{} y^{\prime } = -y^{3}+a \,{\mathrm e}^{\lambda x} y^{2}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime } = -y^{3}+3 a^{2} {\mathrm e}^{2 \lambda x} y-2 a^{3} {\mathrm e}^{3 \lambda x}+a \lambda \,{\mathrm e}^{\lambda x}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime } = -\frac {{\mathrm e}^{2 \lambda x} y^{3}}{3 \lambda }+\frac {2 \lambda ^{2} {\mathrm e}^{-\lambda x}}{3}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime } = a \,{\mathrm e}^{2 \lambda x} y^{3}+b \,{\mathrm e}^{\lambda x} y^{2}+c y+d \,{\mathrm e}^{-\lambda x}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime } = a \,{\mathrm e}^{\lambda x} y^{3}+3 a b \,{\mathrm e}^{\lambda x} y^{2}+c y-2 a \,b^{3} {\mathrm e}^{\lambda x}+b c
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime } = a \,{\mathrm e}^{\lambda x} y^{3}+3 a b \,{\mathrm e}^{\left (\lambda +\mu \right ) x} y^{2}-2 a \,b^{3} {\mathrm e}^{\left (\lambda +3 \mu \right ) x}-b \mu \,{\mathrm e}^{x \mu }
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }+a y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }-\left (a x +b \right ) y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }-\left (a^{2} x^{2}+a \right ) y = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }-\left (x^{2} a +b \right ) y = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }+a^{3} x \left (-a x +2\right ) y = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }-\left (x^{2} a +b c x \right ) y = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }-a \,x^{n} y = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }-a \left (a \,x^{2 n}+n \,x^{n -1}\right ) y = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }-a \,x^{n -2} \left (a \,x^{n}+n +1\right ) y = 0
\]
|
✗ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }+\left (a \,x^{2 n}+b \,x^{n -1}\right ) y = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} b y+a y^{\prime }+y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }+a y^{\prime }+\left (b x +c \right ) y = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }+a y^{\prime }-\left (b \,x^{2}+c \right ) y = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }+a y^{\prime }+b \left (-b \,x^{2}+a x +1\right ) y = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }+a y^{\prime }+b x \left (-b \,x^{3}+a x +2\right ) y = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }+a y^{\prime }+b \left (-b \,x^{2 n}+a \,x^{n}+n \,x^{n -1}\right ) y = 0
\]
|
✗ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }+a y^{\prime }+b \left (-b \,x^{2 n}-a \,x^{n}+n \,x^{n -1}\right ) y = 0
\]
|
✗ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }+x y^{\prime }+\left (n -1\right ) y = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} 2 n y-2 x y^{\prime }+y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} b y+a x y^{\prime }+y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }+a x y^{\prime }+b x y = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }+a x y^{\prime }+\left (b x +c \right ) y = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }+2 a x y^{\prime }+\left (x^{4} b +a^{2} x^{2}+c x +a \right ) y = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }+\left (a x +b \right ) y^{\prime }-a y = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }+\left (a x +b \right ) y^{\prime }+a y = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }+\left (a x +b \right ) y^{\prime }+c \left (a x +b -c \right ) y = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }+\left (a x +2 b \right ) y^{\prime }+\left (a b x +b^{2}-a \right ) y = 0
\]
|
✓ |
✓ |
✗ |
|