82.13.2 problem Ex. 2

Internal problem ID [18802]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter III. Equations of the first order but not of the first degree. Problems at page 32
Problem number : Ex. 2
Date solved : Tuesday, January 28, 2025 at 12:18:36 PM
CAS classification : [_quadrature]

\begin{align*} {y^{\prime }}^{2}-a \,x^{3}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.017 (sec). Leaf size: 31

dsolve(diff(y(x),x)^2-a*x^3=0,y(x), singsol=all)
 

\begin{align*} y \left (x \right ) &= \frac {2 x^{2} \sqrt {a x}}{5}+c_{1} \\ y \left (x \right ) &= -\frac {2 x^{2} \sqrt {a x}}{5}+c_{1} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 43

DSolve[D[y[x],x]^2-a*x^3==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\frac {2}{5} \sqrt {a} x^{5/2}+c_1 \\ y(x)\to \frac {2}{5} \sqrt {a} x^{5/2}+c_1 \\ \end{align*}