Problems 501 to 514

Table 4.883: Second order, non-linear and homogeneous


#	ODE	Mathematica	Maple	Sympy

19349	\[ {} -a y^{\prime \prime } = \left (1+{y^{\prime }}^{2}\right )^{{3}/{2}} \]	✓	✓	✗

19350	\[ {} \sin \left (y\right )^{3} y^{\prime \prime } = \cos \left (y\right ) \]	✓	✓	✓

19354	\[ {} y^{\prime \prime } y+\sqrt {{y^{\prime }}^{2}+a^{2} {y^{\prime \prime }}^{2}} = {y^{\prime }}^{2} \]	✗	✓	✗

19402	\[ {} x^{2} y y^{\prime \prime }+\left (x y^{\prime }-y\right )^{2} = 0 \]	✓	✓	✗

19511	\[ {} 2 x^{2} y y^{\prime \prime }+4 y^{2} = x^{2} {y^{\prime }}^{2}+2 x y y^{\prime } \]	✓	✓	✗

19520	\[ {} x^{2} y y^{\prime \prime }+\left (x y^{\prime }-y\right )^{2}-3 y^{2} = 0 \]	✓	✓	✗

19521	\[ {} y+3 x y^{\prime }+2 y {y^{\prime }}^{2}+\left (x^{2}+2 y^{2} y^{\prime }\right ) y^{\prime \prime } = 0 \]	✗	✗	✗

19522	\[ {} \left (y^{2}+2 x^{2} y^{\prime }\right ) y^{\prime \prime }+2 {y^{\prime }}^{2} \left (x +y\right )+x y^{\prime }+y = 0 \]	✗	✗	✗

19526	\[ {} y^{\prime \prime }+y^{\prime }+{y^{\prime }}^{3} = 0 \]	✓	✓	✓

19528	\[ {} y \left (1-\ln \left (y\right )\right ) y^{\prime \prime }+\left (1+\ln \left (y\right )\right ) {y^{\prime }}^{2} = 0 \]	✓	✓	✗

19529	\[ {} y^{\prime \prime } y-{y^{\prime }}^{2} = y^{2} \ln \left (y\right ) \]	✓	✓	✗

19530	\[ {} y^{\prime }-y^{\prime \prime } y = n \sqrt {{y^{\prime }}^{2}+a^{2} y^{\prime \prime }} \]	✗	✗	✗

19533	\[ {} x^{4} y^{\prime \prime } = \left (y-x y^{\prime }\right )^{3} \]	✓	✓	✗

19534	\[ {} x y^{\prime \prime }+2 y^{\prime } = x^{2} y^{\prime }-y^{2} \]	✗	✗	✗