29.26.13 problem 749

Internal problem ID [5334]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 26
Problem number : 749
Date solved : Monday, January 27, 2025 at 11:15:41 AM
CAS classification : [_quadrature]

\begin{align*} {y^{\prime }}^{2}&=y \end{align*}

✓ Solution by Maple

Time used: 0.035 (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: 0.042 (sec). Leaf size: 36

DSolve[(D[y[x],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*}