Internal problem ID [3481]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 26
Problem number: 748.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {\left (y^{\prime }\right )^{2}-a \,x^{n}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.172 (sec). Leaf size: 41
dsolve(diff(y(x),x)^2 = a*x^n,y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {2 x \sqrt {a \,x^{n}}}{n +2}+c_{1} \\ y \relax (x ) = -\frac {2 x \sqrt {a \,x^{n}}}{n +2}+c_{1} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 57
DSolve[(y'[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*}