29.26.12 problem 748

Internal problem ID [5333]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 26
Problem number : 748
Date solved : Monday, January 27, 2025 at 11:15:40 AM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.041 (sec). Leaf size: 51

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

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

✓ Solution by Mathematica

Time used: 0.008 (sec). Leaf size: 57

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

\begin{align*} y(x)\to -\frac {2 \sqrt {a} x^{\frac {n}{2}+1}}{n+2}+c_1 \\ y(x)\to \frac {2 \sqrt {a} x^{\frac {n}{2}+1}}{n+2}+c_1 \\ \end{align*}