Internal problem ID [9358]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 6, non-linear second order
Problem number: 1780 (book 6.189).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{2} y^{\prime \prime }+y \left (y^{\prime }\right )^{2}+x a=0} \end {gather*}
✓ Solution by Maple
Time used: 0.14 (sec). Leaf size: 115
dsolve(y(x)^2*diff(diff(y(x),x),x)+y(x)*diff(y(x),x)^2+a*x=0,y(x), singsol=all)
\[ \ln \relax (x )-\frac {\int _{}^{\frac {y \relax (x )}{x}}\frac {\textit {\_g}^{2} \left (3 \left (\frac {a}{\textit {\_g}^{3}}\right )^{\frac {1}{3}} \tan \left (\RootOf \left (-2 \textit {\_Z} \sqrt {3}+\ln \left (\frac {\tan ^{2}\left (\textit {\_Z} \right )+1}{3+2 \sqrt {3}\, \tan \left (\textit {\_Z} \right )+\tan ^{2}\left (\textit {\_Z} \right )}\right )+6 c_{1}+6 \left (\int \frac {\left (\frac {a}{\textit {\_g}^{3}}\right )^{\frac {2}{3}} \textit {\_g}^{2}}{\textit {\_g}^{3}+a}d \textit {\_g} \right )\right )\right )+\left (\frac {a}{\textit {\_g}^{3}}\right )^{\frac {1}{3}} \sqrt {3}-2 \sqrt {3}\right )}{\textit {\_g}^{3}+a}d \textit {\_g}}{2 \sqrt {3}}-c_{2} = 0 \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[a*x + y[x]*y'[x]^2 + y[x]^2*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
Not solved