Internal problem ID [9355]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 6, non-linear second order
Problem number: 1781 (book 6.190).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{2} y^{\prime \prime }+y {y^{\prime }}^{2}-a x -b=0} \]
✓ Solution by Maple
Time used: 0.203 (sec). Leaf size: 174
dsolve(y(x)^2*diff(diff(y(x),x),x)+y(x)*diff(y(x),x)^2-a*x-b=0,y(x), singsol=all)
\[ y \left (x \right ) = \operatorname {RootOf}\left (\sqrt {3}\, b \left (\int _{}^{\textit {\_Z}}-\frac {\textit {\_g}^{2} \left (-3 b \left (-\frac {a}{\textit {\_g}^{3} b^{3}}\right )^{\frac {1}{3}} \tan \left (\operatorname {RootOf}\left (-2 b^{2} \left (-\frac {a}{\textit {\_g}^{3} b^{3}}\right )^{\frac {2}{3}} \textit {\_g}^{2} \left (\munderset {\textit {\_R} =\operatorname {RootOf}\left (a^{2} \textit {\_Z}^{3}-1\right )}{\sum }\frac {\ln \left (\textit {\_g} -\textit {\_R} \right )}{\textit {\_R}^{2}}\right )+2 \textit {\_Z} \sqrt {3}\, a^{2}-\ln \left (\frac {1}{2 \sqrt {3}\, \sin \left (\textit {\_Z} \right ) \cos \left (\textit {\_Z} \right )+2 \cos \left (\textit {\_Z} \right )^{2}+1}\right ) a^{2}-6 c_{1} a^{2}\right )\right )-\left (-\frac {a}{\textit {\_g}^{3} b^{3}}\right )^{\frac {1}{3}} \sqrt {3}\, b +2 \sqrt {3}\, a \right )}{\textit {\_g}^{3} a^{2}-1}d \textit {\_g} \right ) a -6 b \ln \left (a x +b \right )+6 c_{2} a \right ) \left (a x +b \right ) \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[-b - a*x + y[x]*y'[x]^2 + y[x]^2*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
Not solved