Internal problem ID [3990]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 26
Problem number: 749.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_quadrature]
\[ \boxed {{y^{\prime }}^{2}-y=0} \]
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 23
dsolve(diff(y(x),x)^2 = y(x),y(x), singsol=all)
\begin{align*} y \left (x \right ) = 0 y \left (x \right ) = \frac {1}{4} c_{1}^{2}-\frac {1}{2} c_{1} x +\frac {1}{4} x^{2} \end{align*}
✓ Solution by Mathematica
Time used: 0.061 (sec). Leaf size: 36
DSolve[(y'[x])^2 == y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{4} (x-c_1){}^2 y(x)\to \frac {1}{4} (x+c_1){}^2 y(x)\to 0 \end{align*}