Problems 601 to 671

Table 4.557: Second order non-linear ODE


#	ODE	Mathematica	Maple	Sympy

18622	\[ {} y^{\prime \prime } = \frac {1}{y^{2}} \]	✓	✓	✓

18623	\[ {} y y^{\prime \prime }-{y^{\prime }}^{2} = 0 \]	✓	✓	✗

18624	\[ {} y y^{\prime \prime }-{y^{\prime }}^{2} = 1 \]	✓	✓	✗

18625	\[ {} \left (x^{2}+1\right ) y^{\prime \prime }-1-{y^{\prime }}^{2} = 0 \]	✓	✓	✓

18873	\[ {} y^{\prime \prime } y^{\prime }-x^{2} y y^{\prime } = x y^{2} \]	✗	✗	✗

18874	\[ {} x^{2} y y^{\prime \prime }+\left (x y^{\prime }-y\right )^{2}-3 y^{2} = 0 \]	✓	✓	✗

18879	\[ {} y^{\prime \prime } = \frac {1}{\sqrt {a y}} \]	✓	✓	✗

18880	\[ {} y^{\prime \prime }+\frac {a^{2}}{y^{2}} = 0 \]	✓	✓	✓

18881	\[ {} y^{\prime \prime }-\frac {a^{2}}{y^{2}} = 0 \]	✓	✓	✓

18883	\[ {} y^{\prime \prime } = \sqrt {1+{y^{\prime }}^{2}} \]	✓	✓	✗

18884	\[ {} \left (x^{2}+1\right ) y^{\prime \prime }+1+{y^{\prime }}^{2} = 0 \]	✓	✓	✓

18886	\[ {} y^{\prime \prime }-a {y^{\prime }}^{2} = 0 \]	✓	✓	✓

18887	\[ {} {y^{\prime }}^{2}+y y^{\prime \prime } = 1 \]	✓	✓	✗

18888	\[ {} y y^{\prime \prime }-{y^{\prime }}^{2} = y^{2} \ln \left (y\right ) \]	✓	✓	✗

18889	\[ {} y^{\prime \prime }+2 y^{\prime }+4 {y^{\prime }}^{3} = 0 \]	✓	✓	✓

18893	\[ {} a^{2} y^{\prime \prime } y^{\prime } = x \]	✓	✓	✓

18894	\[ {} a y^{\prime \prime } = \sqrt {1+{y^{\prime }}^{2}} \]	✓	✓	✗

18903	\[ {} \left (y^{2}+2 x^{2} y^{\prime }\right ) y^{\prime \prime }+2 {y^{\prime }}^{2} \left (x +y\right )+x y^{\prime }+y = 0 \]	✗	✗	✗

18908	\[ {} {y^{\prime }}^{2}-y y^{\prime \prime } = n \sqrt {{y^{\prime }}^{2}+a^{2} {y^{\prime \prime }}^{2}} \]	✗	✓	✗

18910	\[ {} y^{\prime \prime }+y^{\prime }+{y^{\prime }}^{3} = 0 \]	✓	✓	✓

18915	\[ {} y \left (1-\ln \left (y\right )\right ) y^{\prime \prime }+\left (1+\ln \left (y\right )\right ) {y^{\prime }}^{2} = 0 \]	✓	✓	✗

18921	\[ {} y^{3} y^{\prime \prime } = a \]	✓	✓	✓

18923	\[ {} y^{\prime \prime } = a^{2}+k^{2} {y^{\prime }}^{2} \]	✓	✓	✓

18929	\[ {} a^{2} {y^{\prime \prime }}^{2} = 1+{y^{\prime }}^{2} \]	✓	✓	✗

18954	\[ {} x^{2} y y^{\prime \prime }+\left (x y^{\prime }-y\right )^{2} = 0 \]	✓	✓	✗

18955	\[ {} y y^{\prime \prime }+{y^{\prime }}^{2}+1 = 0 \]	✓	✓	✗

19278	\[ {} x y y^{\prime \prime }+x {y^{\prime }}^{2}+y y^{\prime } = 0 \]	✓	✓	✗

19296	\[ {} y^{3} y^{\prime \prime } = a \]	✓	✓	✓

19298	\[ {} y^{\prime \prime }+\frac {a^{2}}{y} = 0 \]	✓	✓	✗

19299	\[ {} y^{\prime \prime } = y^{3}-y \]	✓	✓	✗

19300	\[ {} y^{\prime \prime } = {\mathrm e}^{2 y} \]	✓	✓	✗

19302	\[ {} y^{\prime \prime } = \sqrt {1+{y^{\prime }}^{2}} \]	✓	✓	✗

19309	\[ {} x y^{\prime \prime }+x {y^{\prime }}^{2}-y^{\prime } = 0 \]	✓	✓	✓

19314	\[ {} y^{\prime \prime }+y y^{\prime } = 0 \]	✓	✓	✗

19315	\[ {} {y^{\prime }}^{2}+y y^{\prime \prime } = 1 \]	✓	✓	✗

19316	\[ {} y y^{\prime \prime }-{y^{\prime }}^{2}+y^{\prime } = 0 \]	✓	✓	✗

19317	\[ {} y^{\prime \prime }+2 y^{\prime }+4 {y^{\prime }}^{2} = 0 \]	✓	✓	✓

19318	\[ {} y^{\prime \prime } = a {y^{\prime }}^{2} \]	✓	✓	✓

19319	\[ {} y y^{\prime \prime }+{y^{\prime }}^{2}+1 = 0 \]	✓	✓	✗

19320	\[ {} y y^{\prime \prime }+\sqrt {{y^{\prime }}^{2}+a^{2} {y^{\prime \prime }}^{2}} = {y^{\prime }}^{2} \]	✗	✓	✗

19322	\[ {} a^{2} y^{\prime \prime } y^{\prime } = x \]	✓	✓	✓

19324	\[ {} y^{\prime \prime } = 1+{y^{\prime }}^{2} \]	✓	✓	✓

19325	\[ {} a y^{\prime \prime } = \sqrt {1+{y^{\prime }}^{2}} \]	✓	✓	✗

19326	\[ {} y^{\prime \prime } = a^{2}+k^{2} {y^{\prime }}^{2} \]	✓	✓	✓

19327	\[ {} a^{2} {y^{\prime \prime }}^{2} = 1+{y^{\prime }}^{2} \]	✓	✓	✗

19328	\[ {} y^{\prime \prime }+{y^{\prime }}^{2}+1 = 0 \]	✓	✓	✓

19329	\[ {} y^{\prime } = x y^{\prime \prime }+\sqrt {1+{y^{\prime }}^{2}} \]	✓	✓	✗

19336	\[ {} x y y^{\prime \prime }+x {y^{\prime }}^{2} = 3 y y^{\prime } \]	✓	✓	✗

19337	\[ {} 2 x^{2} y y^{\prime \prime }+y^{2} = x^{2} {y^{\prime }}^{2} \]	✓	✓	✗

19338	\[ {} x^{2} y^{\prime \prime } = \sqrt {m \,x^{2} {y^{\prime }}^{3}+n y^{2}} \]	✗	✗	✗

19339	\[ {} x^{4} y^{\prime \prime } = \left (x^{3}+2 x y\right ) y^{\prime }-4 y^{2} \]	✓	✓	✗

19340	\[ {} x^{4} y^{\prime \prime }-x^{3} y^{\prime } = x^{2} {y^{\prime }}^{2}-4 y^{2} \]	✓	✓	✗

19341	\[ {} x^{2} y^{\prime \prime }+4 y^{2}-6 y = x^{4} {y^{\prime }}^{2} \]	✗	✗	✗

19342	\[ {} y^{\prime \prime } = {\mathrm e}^{y} \]	✓	✓	✓

19347	\[ {} y^{\prime \prime } = \frac {1}{\sqrt {a y}} \]	✓	✓	✗

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

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

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

19519	\[ {} 2 x^{2} \cos \left (y\right ) y^{\prime \prime }-2 x^{2} \sin \left (y\right ) {y^{\prime }}^{2}+x \cos \left (y\right ) y^{\prime }-\sin \left (y\right ) = \ln \left (x \right ) \]	✓	✓	✗

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

19527	\[ {} \left (x^{2}+1\right ) y^{\prime \prime }+1+{y^{\prime }}^{2} = 0 \]	✓	✓	✓

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

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

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

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

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

4.6.7 Problems 601 to 671