Internal problem ID [9327]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 6, non-linear second order
Problem number: 1749 (book 6.158).
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}+4 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.062 (sec). Leaf size: 67
dsolve(4*diff(diff(y(x),x),x)*y(x)-3*diff(y(x),x)^2+4*y(x)=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = 0 \\ -\frac {4 \sqrt {y \relax (x )^{\frac {3}{2}} c_{1}+4 y \relax (x )}}{\sqrt {y \relax (x )}\, c_{1}}-x -c_{2} = 0 \\ \frac {4 \sqrt {y \relax (x )^{\frac {3}{2}} c_{1}+4 y \relax (x )}}{\sqrt {y \relax (x )}\, c_{1}}-x -c_{2} = 0 \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.188 (sec). Leaf size: 28
DSolve[4*y[x] - 3*y'[x]^2 + 4*y[x]*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {\left (-64+c_1{}^2 (x+c_2){}^2\right ){}^2}{256 c_1{}^2} \\ \end{align*}