Internal problem ID [10080]
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]]
\[ \boxed {4 y^{\prime \prime } y-3 {y^{\prime }}^{2}+4 y=0} \]
✓ Solution by Maple
Time used: 0.078 (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 \left (x \right ) = 0 -\frac {4 \sqrt {c_{1} y \left (x \right )^{\frac {3}{2}}+4 y \left (x \right )}}{\sqrt {y \left (x \right )}\, c_{1}}-x -c_{2} = 0 \frac {4 \sqrt {c_{1} y \left (x \right )^{\frac {3}{2}}+4 y \left (x \right )}}{\sqrt {y \left (x \right )}\, c_{1}}-x -c_{2} = 0 \end{align*}
✓ Solution by Mathematica
Time used: 0.587 (sec). Leaf size: 43
DSolve[4*y[x] - 3*y'[x]^2 + 4*y[x]*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {\left (c_1{}^2 x^2+2 c_2 c_1{}^2 x-64+c_2{}^2 c_1{}^2\right ){}^2}{256 c_1{}^2} \]