57.1.49 problem 49

Internal problem ID [9033]
Book : First order enumerated odes
Section : section 1
Problem number : 49
Date solved : Monday, January 27, 2025 at 05:27:42 PM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.028 (sec). Leaf size: 21

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

\begin{align*} y &= \frac {2 x^{{3}/{2}}}{3}+c_{1} \\ y &= -\frac {2 x^{{3}/{2}}}{3}+c_{1} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 33

DSolve[(D[y[x],x])^2==x,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\frac {2 x^{3/2}}{3}+c_1 \\ y(x)\to \frac {2 x^{3/2}}{3}+c_1 \\ \end{align*}