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# |
ODE |
Mathematica |
Maple |
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\[
{}y {y^{\prime \prime }}^{2}-a \,{\mathrm e}^{2 x} = 0
\] |
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\[
{}\left (y^{2}-x^{2} {y^{\prime }}^{2}+x^{2} y y^{\prime \prime }\right )^{2}-4 x y \left (x y^{\prime }-y\right )^{3} = 0
\] |
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\[
{}\left (2 y y^{\prime \prime }-{y^{\prime }}^{2}\right )^{3}+32 y^{\prime \prime } \left (x y^{\prime \prime }-y^{\prime }\right )^{3} = 0
\] |
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\[
{}\sqrt {a {y^{\prime \prime }}^{2}+b {y^{\prime }}^{2}}+c y y^{\prime \prime }+d {y^{\prime }}^{2} = 0
\] |
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\[
{}y^{\prime \prime \prime }+y y^{\prime \prime }-{y^{\prime }}^{2}+1 = 0
\] |
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\[
{}y^{\prime \prime \prime }-y y^{\prime \prime }+{y^{\prime }}^{2} = 0
\] |
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\[
{}y^{\prime \prime \prime }+a y y^{\prime \prime } = 0
\] |
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\[
{}x^{2} y^{\prime \prime \prime }+x y^{\prime \prime }+\left (2 x y-1\right ) y^{\prime }+y^{2}-f \left (x \right ) = 0
\] |
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\[
{}y^{\prime } y^{\prime \prime \prime \prime }-y^{\prime \prime } y^{\prime \prime \prime }+{y^{\prime }}^{3} y^{\prime \prime \prime } = 0
\] |
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\[
{}y^{\prime } \left (f^{\prime \prime \prime }\left (x \right ) y^{\prime }+3 f^{\prime \prime }\left (x \right ) y^{\prime \prime }+3 f^{\prime }\left (x \right ) y^{\prime \prime \prime }+f \left (x \right ) y^{\prime \prime \prime \prime }\right )-y^{\prime \prime } f y^{\prime \prime \prime }+{y^{\prime }}^{3} \left (f^{\prime }\left (x \right ) y^{\prime }+f \left (x \right ) y^{\prime \prime }\right )+2 q \left (x \right ) {y^{\prime }}^{2} \sin \left (y\right )+\left (q \left (x \right ) y^{\prime \prime }-q^{\prime }\left (x \right ) y^{\prime }\right ) \cos \left (y\right ) = 0
\] |
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\[
{}y^{\prime \prime \prime } = f \left (y\right )
\] |
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\[
{}\left [x^{\prime \prime }\left (t \right ) = \left (3 \cos \left (a t +b \right )^{2}-1\right ) c^{2} x \left (t \right )+\frac {3 c^{2} y \left (t \right ) \sin \left (2 a t b \right )}{2}, y^{\prime \prime }\left (t \right ) = \left (3 \sin \left (a t +b \right )^{2}-1\right ) c^{2} y \left (t \right )+\frac {3 c^{2} x \left (t \right ) \sin \left (2 a t b \right )}{2}\right ]
\] |
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\[
{}[x^{\prime }\left (t \right ) = h \left (t \right ) y \left (t \right )-g \left (t \right ) z \left (t \right ), y^{\prime }\left (t \right ) = f \left (t \right ) z \left (t \right )-h \left (t \right ) x \left (t \right ), z^{\prime }\left (t \right ) = g \left (t \right ) x \left (t \right )-f \left (t \right ) y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = x \left (t \right ) \left (a \left (p x \left (t \right )+q y \left (t \right )\right )+\alpha \right ), y^{\prime }\left (t \right ) = y \left (t \right ) \left (\beta +b \left (p x \left (t \right )+q y \left (t \right )\right )\right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = -x \left (t \right ) y \left (t \right )^{2}+x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )^{2} y \left (t \right )-x \left (t \right )-y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right )-x \left (t \right ) \left (x \left (t \right )^{2}+y \left (t \right )^{2}\right ), y^{\prime }\left (t \right ) = -x \left (t \right )+y \left (t \right )-y \left (t \right ) \left (x \left (t \right )^{2}+y \left (t \right )^{2}\right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = -y \left (t \right )+x \left (t \right ) \left (x \left (t \right )^{2}+y \left (t \right )^{2}-1\right ), y^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right ) \left (x \left (t \right )^{2}+y \left (t \right )^{2}-1\right )]
\] |
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\[
{}\left [x^{\prime }\left (t \right ) = -y \left (t \right ) \left (x \left (t \right )^{2}+y \left (t \right )^{2}\right ), y^{\prime }\left (t \right ) = \left \{\begin {array}{cc} x \left (t \right )^{2}+y \left (t \right )^{2} & 2 x \left (t \right )\le x \left (t \right )^{2}+y \left (t \right )^{2} \\ \left (\frac {x \left (t \right )}{2}-\frac {y \left (t \right )^{2}}{2 x \left (t \right )}\right ) \left (x \left (t \right )^{2}+y \left (t \right )^{2}\right ) & \operatorname {otherwise} \end {array}\right .\right ]
\] |
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\[
{}\left [x^{\prime }\left (t \right ) = -y \left (t \right )+\left (\left \{\begin {array}{cc} x \left (t \right ) \left (x \left (t \right )^{2}+y \left (t \right )^{2}-1\right ) \sin \left (\frac {1}{x \left (t \right )^{2}+y \left (t \right )^{2}}\right ) & x \left (t \right )^{2}+y \left (t \right )^{2}\neq 1 \\ 0 & \operatorname {otherwise} \end {array}\right .\right ), y^{\prime }\left (t \right ) = x \left (t \right )+\left (\left \{\begin {array}{cc} y \left (t \right ) \left (x \left (t \right )^{2}+y \left (t \right )^{2}-1\right ) \sin \left (\frac {1}{x \left (t \right )^{2}+y \left (t \right )^{2}}\right ) & x \left (t \right )^{2}+y \left (t \right )^{2}\neq 1 \\ 0 & \operatorname {otherwise} \end {array}\right .\right )\right ]
\] |
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\[
{}\left [x^{\prime \prime }\left (t \right ) = a \,{\mathrm e}^{2 x \left (t \right )}-{\mathrm e}^{-x \left (t \right )}+{\mathrm e}^{-2 x \left (t \right )} \cos \left (y \left (t \right )\right )^{2}, y^{\prime \prime }\left (t \right ) = {\mathrm e}^{-2 x \left (t \right )} \sin \left (y \left (t \right )\right ) \cos \left (y \left (t \right )\right )-\frac {\sin \left (y \left (t \right )\right )}{\cos \left (y \left (t \right )\right )^{3}}\right ]
\] |
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\[
{}\left [x^{\prime \prime }\left (t \right ) = \frac {k x \left (t \right )}{\left (x \left (t \right )^{2}+y \left (t \right )^{2}\right )^{{3}/{2}}}, y^{\prime \prime }\left (t \right ) = \frac {k y \left (t \right )}{\left (x \left (t \right )^{2}+y \left (t \right )^{2}\right )^{{3}/{2}}}\right ]
\] |
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\[
{}[x^{\prime }\left (t \right ) = x \left (t \right ) \left (y \left (t \right )-z \left (t \right )\right ), y^{\prime }\left (t \right ) = y \left (t \right ) \left (z \left (t \right )-x \left (t \right )\right ), z^{\prime }\left (t \right ) = z \left (t \right ) \left (x \left (t \right )-y \left (t \right )\right )]
\] |
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\[
{}\left [x^{\prime }\left (t \right ) = \frac {x \left (t \right )^{2}}{2}-\frac {y \left (t \right )}{24}, y^{\prime }\left (t \right ) = 2 x \left (t \right ) y \left (t \right )-3 z \left (t \right ), z^{\prime }\left (t \right ) = 3 x \left (t \right ) z \left (t \right )-\frac {y \left (t \right )^{2}}{6}\right ]
\] |
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\[
{}[x^{\prime }\left (t \right ) = x \left (t \right ) \left (y \left (t \right )^{2}-z \left (t \right )^{2}\right ), y^{\prime }\left (t \right ) = y \left (t \right ) \left (z \left (t \right )^{2}-x \left (t \right )^{2}\right ), z^{\prime }\left (t \right ) = z \left (t \right ) \left (x \left (t \right )^{2}-y \left (t \right )^{2}\right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = -x \left (t \right ) y \left (t \right )^{2}+x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )^{2} y \left (t \right )-x \left (t \right )-y \left (t \right ), z^{\prime }\left (t \right ) = y \left (t \right )^{2}-x \left (t \right )^{2}]
\] |
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\[
{}[x_{1}^{\prime }\left (t \right ) \sin \left (x_{2} \left (t \right )\right ) = x_{4} \left (t \right ) \sin \left (x_{3} \left (t \right )\right )+x_{5} \left (t \right ) \cos \left (x_{3} \left (t \right )\right ), x_{2}^{\prime }\left (t \right ) = x_{4} \left (t \right ) \cos \left (x_{3} \left (t \right )\right )-x_{5} \left (t \right ) \sin \left (x_{3} \left (t \right )\right ), x_{3}^{\prime }\left (t \right )+x_{1}^{\prime }\left (t \right ) \cos \left (x_{2} \left (t \right )\right ) = a, x_{4}^{\prime }\left (t \right )-\left (1-\lambda \right ) a x_{5} \left (t \right ) = -m \sin \left (x_{2} \left (t \right )\right ) \cos \left (x_{3} \left (t \right )\right ), x_{5}^{\prime }\left (t \right )+\left (1-\lambda \right ) a x_{4} \left (t \right ) = m \sin \left (x_{2} \left (t \right )\right ) \sin \left (x_{3} \left (t \right )\right )]
\] |
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\[
{}y^{\prime } = y^{2}+k \left (a x +b \right )^{n} \left (c x +d \right )^{-n -4}
\] |
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\[
{}x^{2} y^{\prime } = x^{2} y^{2}+a \,x^{2 m} \left (b \,x^{m}+c \right )^{n}-\frac {n^{2}}{4}+\frac {1}{4}
\] |
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\[
{}y^{\prime } = -\left (n +1\right ) x^{n} y^{2}+a \,x^{n +m +1}-a \,x^{m}
\] |
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\[
{}y^{\prime } = a \,x^{n} y^{2}-a \,x^{n} \left (b \,x^{m}+c \right ) y+b m \,x^{m -1}
\] |
✓ |
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\[
{}y^{\prime } = a \,x^{n} y^{2}+b \,x^{m} y+c k \,x^{k -1}-b c \,x^{m +k}-a \,c^{2} x^{n +2 k}
\] |
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\[
{}a \left (x^{2}-1\right ) \left (y^{\prime }+\lambda y^{2}\right )+b x \left (x^{2}-1\right ) y+c \,x^{2}+d x +s = 0
\] |
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\[
{}\left (a \,x^{n}+b \,x^{m}+c \right ) y^{\prime } = a \,x^{n -2} y^{2}+b \,x^{m -1} y+c
\] |
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\[
{}y^{\prime } = b \,{\mathrm e}^{x \mu } y^{2}+a \lambda \,{\mathrm e}^{\lambda x}-a^{2} b \,{\mathrm e}^{\left (\mu +2 \lambda \right ) x}
\] |
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\[
{}y^{\prime } = a \,{\mathrm e}^{k x} y^{2}+b y+c \,{\mathrm e}^{k n x}+d \,{\mathrm e}^{k \left (2 n +1\right ) x}
\] |
✓ |
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\[
{}y^{\prime } = a \,{\mathrm e}^{\lambda x} y^{2}+b n \,x^{n -1}-a \,b^{2} {\mathrm e}^{\lambda x} x^{2 n}
\] |
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\[
{}y^{\prime } = a \,x^{n} y^{2}+b \lambda \,{\mathrm e}^{\lambda x}-a \,b^{2} x^{n} {\mathrm e}^{2 \lambda x}
\] |
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\[
{}y^{\prime } = a \,x^{n} y^{2}-a b \,x^{n} {\mathrm e}^{\lambda x} y+b \lambda \,{\mathrm e}^{\lambda x}
\] |
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\[
{}y^{\prime } = a \,x^{n} y^{2}-a \,x^{n} \left (b \,{\mathrm e}^{\lambda x}+c \right ) y+c \,x^{n}
\] |
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\[
{}y^{\prime } = y^{2}+2 a \lambda x \,{\mathrm e}^{\lambda \,x^{2}}-a^{2} {\mathrm e}^{2 \lambda \,x^{2}}
\] |
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\[
{}y^{\prime } = y^{2}-\lambda ^{2}+a \cosh \left (\lambda x \right )^{n} \sinh \left (\lambda x \right )^{-n -4}
\] |
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\[
{}y^{\prime } = a \ln \left (x \right )^{n} y^{2}+b m \,x^{m -1}-a \,b^{2} x^{2 m} \ln \left (x \right )^{n}
\] |
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\[
{}x y^{\prime } = x y^{2}-a^{2} x \ln \left (\beta x \right )^{2}+a
\] |
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\[
{}x y^{\prime } = x y^{2}-a^{2} x \ln \left (\beta x \right )^{2 k}+a k \ln \left (\beta x \right )^{k -1}
\] |
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\[
{}x y^{\prime } = a \,x^{n} y^{2}+b -a \,b^{2} x^{n} \ln \left (x \right )^{2}
\] |
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\[
{}x^{2} y^{\prime } = x^{2} y^{2}+a \left (b \ln \left (x \right )+c \right )^{n}+\frac {1}{4}
\] |
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\[
{}y^{\prime } = a \,x^{n} y^{2}-a b \,x^{n +1} \ln \left (x \right ) y+b \ln \left (x \right )+b
\] |
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\[
{}y^{\prime } = y^{2}+\lambda ^{2}+c \sin \left (\lambda x +a \right )^{n} \sin \left (\lambda x +b \right )^{-n -4}
\] |
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\[
{}y^{\prime } = y^{2}+a \sin \left (b x \right )^{m} y+a \sin \left (b x \right )^{m}
\] |
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\[
{}y^{\prime } = y^{2}+\lambda ^{2}+c \cos \left (\lambda x +a \right )^{n} \cos \left (\lambda x +b \right )^{-n -4}
\] |
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\[
{}y^{\prime } = y^{2}+a \cos \left (b x \right )^{m} y+a \cos \left (b x \right )^{m}
\] |
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\[
{}y^{\prime } = a \tan \left (\lambda x \right )^{n} y^{2}-a \,b^{2} \tan \left (\lambda x \right )^{n +2}+b \lambda \tan \left (\lambda x \right )^{2}+b \lambda
\] |
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\[
{}y^{\prime } = y^{2}+\lambda ^{2}+c \sin \left (\lambda x \right )^{n} \cos \left (\lambda x \right )^{-n -4}
\] |
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\[
{}y^{\prime } = \lambda \sin \left (\lambda x \right ) y^{2}+a \cos \left (\lambda x \right )^{n} y-a \cos \left (\lambda x \right )^{n -1}
\] |
✓ |
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\[
{}y^{\prime } = y^{2}-2 \lambda ^{2} \tan \left (x \right )^{2}-2 \lambda ^{2} \cot \left (\lambda x \right )^{2}
\] |
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\[
{}y^{\prime } = \lambda \arcsin \left (x \right )^{n} y^{2}-b \lambda \,x^{m} \arcsin \left (x \right )^{n} y+b m \,x^{m -1}
\] |
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\[
{}y^{\prime } = \lambda \arcsin \left (x \right )^{n} y^{2}+\beta m \,x^{m -1}-\lambda \,\beta ^{2} x^{2 m} \arcsin \left (x \right )^{n}
\] |
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\[
{}x y^{\prime } = \left (a \,x^{2 m} y^{2}+b \,x^{n} y+c \right ) \arcsin \left (x \right )^{m}-n y
\] |
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\[
{}y^{\prime } = \lambda \arccos \left (x \right )^{n} y^{2}-b \lambda \,x^{m} \arccos \left (x \right )^{n} y+b m \,x^{m -1}
\] |
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\[
{}y^{\prime } = \lambda \arccos \left (x \right )^{n} y^{2}+\beta m \,x^{m -1}-\lambda \,\beta ^{2} x^{2 m} \arccos \left (x \right )^{n}
\] |
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\[
{}x y^{\prime } = \left (a \,x^{2 m} y^{2}+b \,x^{n} y+c \right ) \arccos \left (x \right )^{m}-n y
\] |
✗ |
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\[
{}y^{\prime } = \lambda \arctan \left (x \right )^{n} y^{2}-b \lambda \,x^{m} \arctan \left (x \right )^{n} y+b m \,x^{m -1}
\] |
✗ |
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\[
{}y^{\prime } = \lambda \arctan \left (x \right )^{n} y^{2}+\beta m \,x^{m -1}-\lambda \,\beta ^{2} x^{2 m} \arctan \left (x \right )^{n}
\] |
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\[
{}x y^{\prime } = \left (a \,x^{2 m} y^{2}+b \,x^{n} y+c \right ) \arctan \left (x \right )^{m}-n y
\] |
✗ |
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\[
{}y^{\prime } = \lambda \operatorname {arccot}\left (x \right )^{n} y^{2}-b \lambda \,x^{m} \operatorname {arccot}\left (x \right )^{n} y+b m \,x^{m -1}
\] |
✗ |
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\[
{}y^{\prime } = \lambda \operatorname {arccot}\left (x \right )^{n} y^{2}+\beta m \,x^{m -1}-\lambda \,\beta ^{2} x^{2 m} \operatorname {arccot}\left (x \right )^{n}
\] |
✗ |
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\[
{}x y^{\prime } = \left (a \,x^{2 m} y^{2}+b \,x^{n} y+c \right ) \operatorname {arccot}\left (x \right )^{m}-n y
\] |
✗ |
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\[
{}y^{\prime } = y^{2} f \left (x \right )-a \,x^{n} f \left (x \right ) y+a n \,x^{n -1}
\] |
✗ |
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\[
{}y^{\prime } = y^{2} f \left (x \right )+a n \,x^{n -1}-a^{2} x^{2 n} f \left (x \right )
\] |
✗ |
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\[
{}y^{\prime } = y^{2} f \left (x \right )+g \left (x \right ) y+a n \,x^{n -1}-a \,x^{n} g \left (x \right )-a^{2} x^{2 n} f \left (x \right )
\] |
✗ |
✗ |
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\[
{}y^{\prime } = y^{2} f \left (x \right )-a \,x^{n} g \left (x \right ) y+a n \,x^{n -1}+a^{2} x^{2 n} \left (g \left (x \right )-f \left (x \right )\right )
\] |
✗ |
✗ |
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\[
{}y^{\prime } = y^{2} f \left (x \right )-a \,{\mathrm e}^{\lambda x} f \left (x \right ) y+a \lambda \,{\mathrm e}^{\lambda x}
\] |
✓ |
✗ |
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\[
{}y^{\prime } = y^{2} f \left (x \right )+a \lambda \,{\mathrm e}^{\lambda x}-a^{2} {\mathrm e}^{2 \lambda x} f \left (x \right )
\] |
✗ |
✗ |
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\[
{}y^{\prime } = y^{2} f \left (x \right )-f \left (x \right ) \left ({\mathrm e}^{\lambda x} a +b \right ) y+a \lambda \,{\mathrm e}^{\lambda x}
\] |
✗ |
✗ |
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\[
{}y^{\prime } = y^{2} f \left (x \right )+g \left (x \right ) y+a \lambda \,{\mathrm e}^{\lambda x}-a \,{\mathrm e}^{\lambda x} g \left (x \right )-a^{2} {\mathrm e}^{2 \lambda x} f \left (x \right )
\] |
✗ |
✗ |
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\[
{}y^{\prime } = y^{2} f \left (x \right )-a \,{\mathrm e}^{\lambda x} g \left (x \right ) y+a \lambda \,{\mathrm e}^{\lambda x}+a^{2} {\mathrm e}^{2 \lambda x} \left (g \left (x \right )-f \left (x \right )\right )
\] |
✗ |
✗ |
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\[
{}y^{\prime } = y^{2} f \left (x \right )+2 a \lambda x \,{\mathrm e}^{\lambda \,x^{2}}-a^{2} f \left (x \right ) {\mathrm e}^{2 \lambda \,x^{2}}
\] |
✗ |
✗ |
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\[
{}y^{\prime } = y^{2} f \left (x \right )+\lambda x y+a f \left (x \right ) {\mathrm e}^{\lambda x}
\] |
✗ |
✗ |
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\[
{}y^{\prime } = y^{2} f \left (x \right )-a \tanh \left (\lambda x \right )^{2} \left (f \left (x \right ) a +\lambda \right )+a \lambda
\] |
✗ |
✗ |
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\[
{}y^{\prime } = y^{2} f \left (x \right )-a \coth \left (\lambda x \right )^{2} \left (f \left (x \right ) a +\lambda \right )+a \lambda
\] |
✗ |
✗ |
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\[
{}y^{\prime } = y^{2} f \left (x \right )-a^{2} f \left (x \right )+a \lambda \sinh \left (\lambda x \right )-a^{2} f \left (x \right ) \sinh \left (\lambda x \right )^{2}
\] |
✗ |
✗ |
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\[
{}x y^{\prime } = y^{2} f \left (x \right )+a -a^{2} f \left (x \right ) \ln \left (x \right )^{2}
\] |
✗ |
✗ |
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\[
{}y^{\prime } = y^{2} f \left (x \right )-a x \ln \left (x \right ) f \left (x \right ) y+a \ln \left (x \right )+a
\] |
✗ |
✗ |
|
|
\[
{}y^{\prime } = y^{2} f \left (x \right )-a^{2} f \left (x \right )+a \lambda \sin \left (\lambda x \right )+a^{2} f \left (x \right ) \sin \left (\lambda x \right )^{2}
\] |
✗ |
✗ |
|
|
\[
{}y^{\prime } = y^{2} f \left (x \right )-a^{2} f \left (x \right )+a \lambda \cos \left (\lambda x \right )+a^{2} f \left (x \right ) \cos \left (\lambda x \right )^{2}
\] |
✗ |
✗ |
|
|
\[
{}y^{\prime } = y^{2} f \left (x \right )-a \tan \left (\lambda x \right )^{2} \left (f \left (x \right ) a -\lambda \right )+a \lambda
\] |
✗ |
✗ |
|
|
\[
{}y^{\prime } = y^{2} f \left (x \right )-a \cot \left (\lambda x \right )^{2} \left (f \left (x \right ) a -\lambda \right )+a \lambda
\] |
✗ |
✗ |
|
|
\[
{}y^{\prime } = y^{2} f \left (x \right )-f \left (x \right ) g \left (x \right ) y+g^{\prime }\left (x \right )
\] |
✗ |
✗ |
|
|
\[
{}f \left (x \right )^{2} y^{\prime }-f^{\prime }\left (x \right ) y^{2}+g \left (x \right ) \left (y-f \left (x \right )\right ) = 0
\] |
✗ |
✗ |
|
|
\[
{}y^{\prime } = y^{2}+a^{2} f \left (a x +b \right )
\] |
✗ |
✗ |
|
|
\[
{}y^{\prime } = y^{2}+\frac {f \left (\frac {1}{x}\right )}{x^{4}}
\] |
✗ |
✗ |
|
|
\[
{}y^{\prime } = y^{2}+\frac {f \left (\frac {a x +b}{c x +d}\right )}{\left (c x +d \right )^{4}}
\] |
✗ |
✗ |
|
|
\[
{}x^{2} y^{\prime } = x^{4} f \left (x \right ) y^{2}+1
\] |
✗ |
✗ |
|
|
\[
{}x^{2} y^{\prime } = y^{2} x^{4}+x^{2 n} f \left (a \,x^{n}+b \right )-\frac {n^{2}}{4}+\frac {1}{4}
\] |
✗ |
✗ |
|
|
\[
{}y^{\prime } = y^{2} f \left (x \right )+g \left (x \right ) y+h \left (x \right )
\] |
✗ |
✗ |
|
|
\[
{}y^{\prime } = y^{2}+{\mathrm e}^{2 \lambda x} f \left ({\mathrm e}^{\lambda x}\right )-\frac {\lambda ^{2}}{4}
\] |
✗ |
✗ |
|
|
\[
{}y^{\prime } = y^{2}-\frac {\lambda ^{2}}{4}+\frac {{\mathrm e}^{2 \lambda x} f \left (\frac {{\mathrm e}^{\lambda x} a +b}{c \,{\mathrm e}^{\lambda x}+d}\right )}{\left (c \,{\mathrm e}^{\lambda x}+d \right )^{4}}
\] |
✗ |
✗ |
|
|
\[
{}y^{\prime } = y^{2}-\lambda ^{2}+\frac {f \left (\coth \left (\lambda x \right )\right )}{\sinh \left (\lambda x \right )^{4}}
\] |
✗ |
✗ |
|
|
\[
{}y^{\prime } = y^{2}-\lambda ^{2}+\frac {f \left (\tanh \left (\lambda x \right )\right )}{\cosh \left (\lambda x \right )^{4}}
\] |
✗ |
✗ |
|
|
\[
{}x^{2} y^{\prime } = x^{2} y^{2}+f \left (a \ln \left (x \right )+b \right )+\frac {1}{4}
\] |
✗ |
✗ |
|