Problems 401 to 500

Table 4.881: Second order, non-linear and homogeneous


#	ODE	Mathematica	Maple	Sympy

16855	\[ {} y^{\prime \prime } = y^{\prime } \ln \left (y^{\prime }\right ) \]	✗	✓	✗

16857	\[ {} y^{\prime \prime } = y^{\prime } \left (1+y^{\prime }\right ) \]	✓	✓	✓

16858	\[ {} 3 y^{\prime \prime } = \left (1+{y^{\prime }}^{2}\right )^{{3}/{2}} \]	✓	✓	✗

16860	\[ {} y^{\prime \prime } y = {y^{\prime }}^{2} \]	✓	✓	✗

16861	\[ {} y^{\prime \prime } = 2 y y^{\prime } \]	✗	✓	✗

16862	\[ {} 3 y^{\prime } y^{\prime \prime } = 2 y \]	✗	✓	✗

16863	\[ {} 2 y^{\prime \prime } = 3 y^{2} \]	✓	✓	✗

16864	\[ {} y^{\prime \prime } y+{y^{\prime }}^{2} = 0 \]	✓	✓	✗

16865	\[ {} y^{\prime \prime } y = y^{\prime }+{y^{\prime }}^{2} \]	✓	✓	✗

16869	\[ {} y^{\prime \prime } y-{y^{\prime }}^{2} = y^{2} y^{\prime } \]	✓	✓	✗

16870	\[ {} y^{\prime \prime } = {\mathrm e}^{2 y} \]	✓	✓	✗

16871	\[ {} 2 y^{\prime \prime } y-3 {y^{\prime }}^{2} = 4 y^{2} \]	✓	✓	✗

17094	\[ {} x^{\prime \prime }+{x^{\prime }}^{2}+x = 0 \]	✓	✓	✗

17095	\[ {} x^{\prime \prime }-2 {x^{\prime }}^{2}+x^{\prime }-2 x = 0 \]	✗	✗	✗

17096	\[ {} x^{\prime \prime }-x \,{\mathrm e}^{x^{\prime }} = 0 \]	✓	✓	✗

17097	\[ {} x^{\prime \prime }+{\mathrm e}^{-x^{\prime }}-x = 0 \]	✗	✗	✗

17098	\[ {} x^{\prime \prime }+x {x^{\prime }}^{2} = 0 \]	✓	✓	✗

17099	\[ {} x^{\prime \prime }+\left (x+2\right ) x^{\prime } = 0 \]	✓	✓	✗

17100	\[ {} x^{\prime \prime }-x^{\prime }+x-x^{2} = 0 \]	✗	✗	✗

17467	\[ {} y^{\prime \prime }+y^{\prime }+y+y^{3} = 0 \]	✗	✗	✗

17470	\[ {} y^{\prime \prime }+\mu \left (1-y^{2}\right ) y^{\prime }+y = 0 \]	✗	✗	✗

17487	\[ {} y y^{\prime \prime }+{y^{\prime }}^{2} = 0 \]	✓	✓	✗

17892	\[ {} y^{\prime \prime } = \frac {1}{\sqrt {y}} \]	✓	✓	✗

17897	\[ {} y^{\prime \prime } y+{y^{\prime }}^{2} = y^{2} \ln \left (y\right ) \]	✓	✓	✗

17898	\[ {} y^{\prime \prime } y-{y^{\prime }}^{2} = 0 \]	✓	✓	✗

17899	\[ {} x y y^{\prime \prime }+x {y^{\prime }}^{2}-y y^{\prime } = 0 \]	✓	✓	✗

17900	\[ {} n \,x^{3} y^{\prime \prime } = \left (y-x y^{\prime }\right )^{2} \]	✓	✓	✗

17903	\[ {} y^{\prime } y^{\prime \prime }-x^{2} y y^{\prime }-x y^{2} = 0 \]	✗	✗	✗

17906	\[ {} y^{\prime \prime } y-{y^{\prime }}^{2}-{y^{\prime }}^{4} = 0 \]	✓	✓	✗

17907	\[ {} a^{2} y^{\prime \prime } = 2 x \sqrt {1+{y^{\prime }}^{2}} \]	✓	✗	✗

17908	\[ {} x^{2} y y^{\prime \prime }+x^{2} {y^{\prime }}^{2}-5 x y y^{\prime } = 4 y^{2} \]	✓	✓	✗

17909	\[ {} y \left (1-\ln \left (y\right )\right ) y^{\prime \prime }+\left (1+\ln \left (y\right )\right ) {y^{\prime }}^{2} = 0 \]	✓	✓	✗

17912	\[ {} {y^{\prime \prime }}^{2}+2 x y^{\prime \prime }-y^{\prime } = 0 \]	✓	✓	✗

17913	\[ {} {y^{\prime \prime }}^{2}-2 x y^{\prime \prime }-y^{\prime } = 0 \]	✓	✓	✗

17965	\[ {} y^{\prime \prime }+2 y^{\prime }+y^{2} = 0 \]	✗	✗	✗

18108	\[ {} y^{\prime \prime } y+{y^{\prime }}^{2} = 0 \]	✓	✓	✗

18109	\[ {} x y^{\prime \prime } = {y^{\prime }}^{3}+y^{\prime } \]	✓	✓	✓

18111	\[ {} x^{2} y^{\prime \prime } = 2 x y^{\prime }+{y^{\prime }}^{2} \]	✓	✓	✓

18113	\[ {} y^{\prime \prime } y-{y^{\prime }}^{2} = 0 \]	✓	✓	✗

18115	\[ {} \left (x^{2}+2 y^{\prime }\right ) y^{\prime \prime }+2 x y^{\prime } = 0 \]	✓	✓	✓

18116	\[ {} y^{\prime \prime } y = y^{2} y^{\prime }+{y^{\prime }}^{2} \]	✓	✓	✗

18117	\[ {} y^{\prime \prime } = y^{\prime } {\mathrm e}^{y} \]	✗	✓	✗

18120	\[ {} y^{\prime \prime } y = {y^{\prime }}^{2} \]	✓	✓	✗

18126	\[ {} y^{\prime \prime } y+{y^{\prime }}^{2}-2 y y^{\prime } = 0 \]	✓	✓	✗

18130	\[ {} y^{\prime \prime }+2 x {y^{\prime }}^{2} = 0 \]	✓	✓	✓

18154	\[ {} x^{2} y^{\prime \prime } = y^{\prime } \left (3 x -2 y^{\prime }\right ) \]	✓	✓	✓

18160	\[ {} y^{2} y^{\prime \prime }+{y^{\prime }}^{3} = 0 \]	✓	✓	✗

18165	\[ {} x^{2} y^{\prime \prime }+{y^{\prime }}^{2} = 0 \]	✓	✓	✓

18168	\[ {} y^{\prime \prime } = 2 y {y^{\prime }}^{3} \]	✓	✓	✗

18191	\[ {} y^{\prime \prime }+{y^{\prime }}^{2} = 0 \]	✓	✓	✓

18408	\[ {} x^{\prime \prime }+\left (5 x^{4}-9 x^{2}\right ) x^{\prime }+x^{5} = 0 \]	✗	✗	✗

18452	\[ {} x^{2} y^{\prime \prime }-\frac {x^{2} {y^{\prime }}^{2}}{2 y}+4 x y^{\prime }+4 y = 0 \]	✓	✓	✗

18457	\[ {} v^{\prime \prime } = \left (\frac {1}{v}+{v^{\prime }}^{4}\right )^{{1}/{3}} \]	✗	✗	✗

18459	\[ {} \sqrt {y^{\prime }+y} = \left (y^{\prime \prime }+2 x \right )^{{1}/{4}} \]	✗	✗	✗

18488	\[ {} y^{\prime \prime } = \frac {m \sqrt {1+{y^{\prime }}^{2}}}{k} \]	✓	✓	✗

18489	\[ {} \phi ^{\prime \prime } = \frac {4 \pi n c}{\sqrt {v_{0}^{2}+\frac {2 e \left (\phi -V_{0} \right )}{m}}} \]	✓	✓	✗

18517	\[ {} y^{\prime \prime } = c \left (1+{y^{\prime }}^{2}\right ) \]	✓	✓	✓

18518	\[ {} y^{\prime \prime } = c \left (1+{y^{\prime }}^{2}\right )^{{3}/{2}} \]	✓	✓	✗

18530	\[ {} y^{\prime \prime }-2 y y^{\prime } = 0 \]	✓	✓	✗

18531	\[ {} y^{\prime \prime }-{y^{\prime }}^{2}-y {y^{\prime }}^{3} = 0 \]	✓	✓	✗

18532	\[ {} \left (1+{y^{\prime }}^{2}\right )^{{3}/{2}} = r y^{\prime \prime } \]	✓	✓	✗

18534	\[ {} \left (1+y^{2}\right ) y^{\prime \prime }-2 y {y^{\prime }}^{2}-2 \left (1+y^{2}\right ) y^{\prime } = y^{2} \left (1+y^{2}\right ) \]	✗	✗	✗

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

4.17.5 Problems 401 to 500