26.13 problem 749

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: 0.078 (sec). Leaf size: 17

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

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