Internal problem ID [9307]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 6, non-linear second order
Problem number: 1729 (book 6.138).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]
Solve \begin {gather*} \boxed {2 y^{\prime \prime } y-\left (y^{\prime }\right )^{2}+a=0} \end {gather*}
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 24
dsolve(2*diff(diff(y(x),x),x)*y(x)-diff(y(x),x)^2+a=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {\left (c_{1}^{2}-a \right ) x^{2}}{4 c_{2}}+c_{1} x +c_{2} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 31
DSolve[a - y'[x]^2 + 2*y[x]*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {x^2 \left (-a+c_1{}^2\right )}{4 c_2}+c_1 x+c_2 \\ \end{align*}