Internal problem ID [9329]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 6, non-linear second order
Problem number: 1750.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
Solve \begin {gather*} \boxed {4 y^{\prime \prime } y-3 \left (y^{\prime }\right )^{2}+a y^{3}+y^{2} b +c y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 87
dsolve(4*diff(diff(y(x),x),x)*y(x)-3*diff(y(x),x)^2+a*y(x)^3+y(x)^2*b+c*y(x)=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = 0 \\ \int _{}^{y \relax (x )}-\frac {3}{\sqrt {9 c_{1} \textit {\_a}^{\frac {3}{2}}-3 \textit {\_a}^{3} a -9 b \,\textit {\_a}^{2}+9 c \textit {\_a}}}d \textit {\_a} -x -c_{2} = 0 \\ \int _{}^{y \relax (x )}\frac {3}{\sqrt {9 c_{1} \textit {\_a}^{\frac {3}{2}}-3 \textit {\_a}^{3} a -9 b \,\textit {\_a}^{2}+9 c \textit {\_a}}}d \textit {\_a} -x -c_{2} = 0 \\ \end{align*}
✓ Solution by Mathematica
Time used: 2.856 (sec). Leaf size: 2281
DSolve[c*y[x] + b*y[x]^2 + a*y[x]^3 - 3*y'[x]^2 + 4*y[x]*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
Too large to display