Internal problem ID [2297]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 35, page 157
Problem number: 25.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]
\[ \boxed {2 y y^{\prime \prime }-{y^{\prime }}^{2}=0} \]
✓ Solution by Maple
Time used: 0.062 (sec). Leaf size: 17
dsolve(2*y(x)*diff(y(x),x$2)-diff(y(x),x)^2=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= 0 \\ y \left (x \right ) &= \frac {\left (c_{1} x +c_{2} \right )^{2}}{4} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.015 (sec). Leaf size: 29
DSolve[2*y[x]*y''[x]-y'[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {(c_1 x+2 c_2){}^2}{4 c_2} \\ y(x)\to \text {Indeterminate} \\ \end{align*}