29.31.27 problem 927

Internal problem ID [5506]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 31
Problem number : 927
Date solved : Monday, January 27, 2025 at 11:34:21 AM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.039 (sec). Leaf size: 37

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

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

✓ Solution by Mathematica

Time used: 0.005 (sec). Leaf size: 39

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

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