60.7.189 problem 1780 (book 6.189)

Internal problem ID [11778]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 6, non-linear second order
Problem number : 1780 (book 6.189)
Date solved : Tuesday, January 28, 2025 at 06:11:22 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{2} y^{\prime \prime }+y {y^{\prime }}^{2}+a x&=0 \end{align*}

✓ Solution by Maple

Time used: 0.164 (sec). Leaf size: 110

dsolve(y(x)^2*diff(diff(y(x),x),x)+y(x)*diff(y(x),x)^2+a*x=0,y(x), singsol=all)
 

\[ \ln \left (x \right )-\frac {\left (\int _{}^{\frac {y}{x}}\frac {\textit {\_g}^{2} \left (\left (\left (\frac {a}{\textit {\_g}^{3}}\right )^{{1}/{3}}-2\right ) \sqrt {3}+3 \left (\frac {a}{\textit {\_g}^{3}}\right )^{{1}/{3}} \tan \left (\operatorname {RootOf}\left (2 \sqrt {3}\, \textit {\_Z} -\ln \left (\frac {1}{\sqrt {3}\, \sin \left (2 \textit {\_Z} \right )+2+\cos \left (2 \textit {\_Z} \right )}\right )-6 c_{1} -6 \left (\int \frac {\left (\frac {a}{\textit {\_g}^{3}}\right )^{{2}/{3}} \textit {\_g}^{2}}{\textit {\_g}^{3}+a}d \textit {\_g} \right )\right )\right )\right )}{\textit {\_g}^{3}+a}d \textit {\_g} \right ) \sqrt {3}}{6}-c_{2} = 0 \]

✗ Solution by Mathematica

Time used: 0.000 (sec). Leaf size: 0

DSolve[a*x + y[x]*D[y[x],x]^2 + y[x]^2*D[y[x],{x,2}] == 0,y[x],x,IncludeSingularSolutions -> True]
 

Not solved