Problems 601 to 671

Table 4.557: Second order non-linear ODE


#	ODE	Mathematica	Maple	Sympy

18630	\[ {} y^{\prime \prime } = \frac {1}{y^{2}} \]	✓	✓	✓

18631	\[ {} y y^{\prime \prime }-{y^{\prime }}^{2} = 0 \]	✓	✓	✗

18632	\[ {} y y^{\prime \prime }-{y^{\prime }}^{2} = 1 \]	✓	✓	✗

18633	\[ {} \left (x^{2}+1\right ) y^{\prime \prime }-1-{y^{\prime }}^{2} = 0 \]	✓	✓	✓

18881	\[ {} y^{\prime \prime } y^{\prime }-x^{2} y y^{\prime } = x y^{2} \]	✗	✗	✗

18882	\[ {} x^{2} y y^{\prime \prime }+\left (x y^{\prime }-y\right )^{2}-3 y^{2} = 0 \]	✓	✓	✗

18887	\[ {} y^{\prime \prime } = \frac {1}{\sqrt {a y}} \]	✓	✓	✗

18888	\[ {} y^{\prime \prime }+\frac {a^{2}}{y^{2}} = 0 \]	✓	✓	✓

18889	\[ {} y^{\prime \prime }-\frac {a^{2}}{y^{2}} = 0 \]	✓	✓	✓

18891	\[ {} y^{\prime \prime } = \sqrt {1+{y^{\prime }}^{2}} \]	✓	✓	✗

18892	\[ {} \left (x^{2}+1\right ) y^{\prime \prime }+1+{y^{\prime }}^{2} = 0 \]	✓	✓	✓

18894	\[ {} y^{\prime \prime }-a {y^{\prime }}^{2} = 0 \]	✓	✓	✓

18895	\[ {} y y^{\prime \prime }+{y^{\prime }}^{2} = 1 \]	✓	✓	✗

18896	\[ {} y y^{\prime \prime }-{y^{\prime }}^{2} = y^{2} \ln \left (y\right ) \]	✓	✓	✗

18897	\[ {} y^{\prime \prime }+2 y^{\prime }+4 {y^{\prime }}^{3} = 0 \]	✓	✓	✓

18901	\[ {} a^{2} y^{\prime \prime } y^{\prime } = x \]	✓	✓	✓

18902	\[ {} a y^{\prime \prime } = \sqrt {1+{y^{\prime }}^{2}} \]	✓	✓	✗

18911	\[ {} \left (y^{2}+2 y^{\prime } x^{2}\right ) y^{\prime \prime }+2 {y^{\prime }}^{2} \left (x +y\right )+x y^{\prime }+y = 0 \]	✗	✗	✗

18916	\[ {} {y^{\prime }}^{2}-y y^{\prime \prime } = n \sqrt {{y^{\prime }}^{2}+a^{2} {y^{\prime \prime }}^{2}} \]	✗	✓	✗

18918	\[ {} y^{\prime \prime }+y^{\prime }+{y^{\prime }}^{3} = 0 \]	✓	✓	✓

18923	\[ {} y \left (1-\ln \left (y\right )\right ) y^{\prime \prime }+\left (1+\ln \left (y\right )\right ) {y^{\prime }}^{2} = 0 \]	✓	✓	✗

18929	\[ {} y^{3} y^{\prime \prime } = a \]	✓	✓	✓

18931	\[ {} y^{\prime \prime } = a^{2}+k^{2} {y^{\prime }}^{2} \]	✓	✓	✓

18937	\[ {} a^{2} {y^{\prime \prime }}^{2} = 1+{y^{\prime }}^{2} \]	✓	✓	✗

18962	\[ {} x^{2} y y^{\prime \prime }+\left (x y^{\prime }-y\right )^{2} = 0 \]	✓	✓	✗

18963	\[ {} y y^{\prime \prime }+1+{y^{\prime }}^{2} = 0 \]	✓	✓	✗

19286	\[ {} x y y^{\prime \prime }+{y^{\prime }}^{2} x +y y^{\prime } = 0 \]	✓	✓	✗

19304	\[ {} y^{3} y^{\prime \prime } = a \]	✓	✓	✓

19306	\[ {} y^{\prime \prime }+\frac {a^{2}}{y} = 0 \]	✓	✓	✗

19307	\[ {} y^{\prime \prime } = y^{3}-y \]	✓	✓	✗

19308	\[ {} y^{\prime \prime } = {\mathrm e}^{2 y} \]	✓	✓	✗

19310	\[ {} y^{\prime \prime } = \sqrt {1+{y^{\prime }}^{2}} \]	✓	✓	✗

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

19322	\[ {} y^{\prime \prime }+y y^{\prime } = 0 \]	✓	✓	✗

19323	\[ {} y y^{\prime \prime }+{y^{\prime }}^{2} = 1 \]	✓	✓	✗

19324	\[ {} y y^{\prime \prime }-{y^{\prime }}^{2}+y^{\prime } = 0 \]	✓	✓	✗

19325	\[ {} y^{\prime \prime }+2 y^{\prime }+4 {y^{\prime }}^{2} = 0 \]	✓	✓	✓

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

19327	\[ {} y y^{\prime \prime }+1+{y^{\prime }}^{2} = 0 \]	✓	✓	✗

19328	\[ {} y y^{\prime \prime }+\sqrt {{y^{\prime }}^{2}+a^{2} {y^{\prime \prime }}^{2}} = {y^{\prime }}^{2} \]	✗	✓	✗

19330	\[ {} a^{2} y^{\prime \prime } y^{\prime } = x \]	✓	✓	✓

19332	\[ {} y^{\prime \prime } = 1+{y^{\prime }}^{2} \]	✓	✓	✓

19333	\[ {} a y^{\prime \prime } = \sqrt {1+{y^{\prime }}^{2}} \]	✓	✓	✗

19334	\[ {} y^{\prime \prime } = a^{2}+k^{2} {y^{\prime }}^{2} \]	✓	✓	✓

19335	\[ {} a^{2} {y^{\prime \prime }}^{2} = 1+{y^{\prime }}^{2} \]	✓	✓	✗

19336	\[ {} y^{\prime \prime }+{y^{\prime }}^{2}+1 = 0 \]	✓	✓	✓

19337	\[ {} y^{\prime } = x y^{\prime \prime }+\sqrt {1+{y^{\prime }}^{2}} \]	✓	✓	✗

19344	\[ {} x y y^{\prime \prime }+{y^{\prime }}^{2} x = 3 y y^{\prime } \]	✓	✓	✗

19345	\[ {} 2 x^{2} y y^{\prime \prime }+y^{2} = x^{2} {y^{\prime }}^{2} \]	✓	✓	✗

19346	\[ {} x^{2} y^{\prime \prime } = \sqrt {m \,x^{2} {y^{\prime }}^{3}+y^{2} n} \]	✗	✗	✗

19347	\[ {} x^{4} y^{\prime \prime } = \left (x^{3}+2 x y\right ) y^{\prime }-4 y^{2} \]	✓	✓	✗

19348	\[ {} x^{4} y^{\prime \prime }-x^{3} y^{\prime } = x^{2} {y^{\prime }}^{2}-4 y^{2} \]	✓	✓	✗

19349	\[ {} x^{2} y^{\prime \prime }+4 y^{2}-6 y = x^{4} {y^{\prime }}^{2} \]	✗	✗	✗

19350	\[ {} y^{\prime \prime } = {\mathrm e}^{y} \]	✓	✓	✓

19355	\[ {} y^{\prime \prime } = \frac {1}{\sqrt {a y}} \]	✓	✓	✗

19357	\[ {} -a y^{\prime \prime } = \left (1+{y^{\prime }}^{2}\right )^{{3}/{2}} \]	✓	✓	✗

19358	\[ {} \sin \left (y\right )^{3} y^{\prime \prime } = \cos \left (y\right ) \]	✓	✓	✓

19362	\[ {} y y^{\prime \prime }+\sqrt {{y^{\prime }}^{2}+a^{2} {y^{\prime \prime }}^{2}} = {y^{\prime }}^{2} \]	✗	✓	✗

19410	\[ {} x^{2} y y^{\prime \prime }+\left (x y^{\prime }-y\right )^{2} = 0 \]	✓	✓	✗

19519	\[ {} 2 x^{2} y y^{\prime \prime }+4 y^{2} = x^{2} {y^{\prime }}^{2}+2 x y y^{\prime } \]	✓	✓	✗

19527	\[ {} 2 x^{2} \cos \left (y\right ) y^{\prime \prime }-2 x^{2} \sin \left (y\right ) {y^{\prime }}^{2}+x \cos \left (y\right ) y^{\prime }-\sin \left (y\right ) = \ln \left (x \right ) \]	✓	✓	✗

19528	\[ {} x^{2} y y^{\prime \prime }+\left (x y^{\prime }-y\right )^{2}-3 y^{2} = 0 \]	✓	✓	✗

19529	\[ {} y+3 x y^{\prime }+2 y {y^{\prime }}^{2}+\left (x^{2}+2 y^{2} y^{\prime }\right ) y^{\prime \prime } = 0 \]	✗	✗	✗

19530	\[ {} \left (y^{2}+2 y^{\prime } x^{2}\right ) y^{\prime \prime }+2 {y^{\prime }}^{2} \left (x +y\right )+x y^{\prime }+y = 0 \]	✗	✗	✗

19534	\[ {} y^{\prime \prime }+y^{\prime }+{y^{\prime }}^{3} = 0 \]	✓	✓	✓

19535	\[ {} \left (x^{2}+1\right ) y^{\prime \prime }+1+{y^{\prime }}^{2} = 0 \]	✓	✓	✓

19536	\[ {} y \left (1-\ln \left (y\right )\right ) y^{\prime \prime }+\left (1+\ln \left (y\right )\right ) {y^{\prime }}^{2} = 0 \]	✓	✓	✗

19537	\[ {} y y^{\prime \prime }-{y^{\prime }}^{2} = y^{2} \ln \left (y\right ) \]	✓	✓	✗

19538	\[ {} y^{\prime }-y y^{\prime \prime } = n \sqrt {{y^{\prime }}^{2}+a^{2} y^{\prime \prime }} \]	✗	✗	✗

19541	\[ {} x^{4} y^{\prime \prime } = \left (y-x y^{\prime }\right )^{3} \]	✓	✓	✗

19542	\[ {} x y^{\prime \prime }+2 y^{\prime } = -y^{2}+y^{\prime } x^{2} \]	✗	✗	✗

4.6.7 Problems 601 to 671