26.13 problem 749

Internal problem ID [3482]

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]

Solve \begin {gather*} \boxed {\left (y^{\prime }\right )^{2}-y=0} \end {gather*}

Solution by Maple

Time used: 0.188 (sec). Leaf size: 23

dsolve(diff(y(x),x)^2 = y(x),y(x), singsol=all)
 

\begin{align*} y \relax (x ) = 0 \\ y \relax (x ) = \frac {1}{4} c_{1}^{2}-\frac {1}{2} c_{1} x +\frac {1}{4} x^{2} \\ \end{align*}

Solution by Mathematica

Time used: 0.039 (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*}