Internal problem ID [9320]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 6, non-linear second order
Problem number: 1742 (book 6.151).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]]
Solve \begin {gather*} \boxed {2 y^{\prime \prime } y-3 \left (y^{\prime }\right )^{2}-4 y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 41
dsolve(2*diff(diff(y(x),x),x)*y(x)-3*diff(y(x),x)^2-4*y(x)^2=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = 0 \\ y \relax (x ) = \frac {4}{c_{1}^{2} \left (\sin ^{2}\relax (x )\right )-c_{2}^{2} \left (\sin ^{2}\relax (x )\right )-2 c_{1} c_{2} \sin \relax (x ) \cos \relax (x )+c_{2}^{2}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.09 (sec). Leaf size: 17
DSolve[-4*y[x]^2 - 3*y'[x]^2 + 2*y[x]*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_2 \sec ^2(x+2 c_1) \\ \end{align*}