Internal problem ID [3989]
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]
\[ \boxed {{y^{\prime }}^{2}=a \,x^{n}} \]
✓ Solution by Maple
Time used: 0.078 (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[(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*}