Internal problem ID [3496]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 26
Problem number: 763.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {\left (y^{\prime }\right )^{2}-a^{2} y^{n}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.062 (sec). Leaf size: 83
dsolve(diff(y(x),x)^2 = a^2*y(x)^n,y(x), singsol=all)
\begin{align*} y \relax (x ) = 2^{\frac {2}{n -2}} \left (\frac {1}{a \left (c_{1} n -n x -2 c_{1}+2 x \right )}\right )^{\frac {2}{n -2}} \\ y \relax (x ) = 2^{\frac {2}{n -2}} \left (\frac {1}{a \left (-c_{1} n +n x +2 c_{1}-2 x \right )}\right )^{\frac {2}{n -2}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 1.78 (sec). Leaf size: 77
DSolve[(y'[x])^2==a^2 y[x]^n,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to 2^{\frac {2}{n-2}} (-((n-2) (a x+c_1))){}^{-\frac {2}{n-2}} \\ y(x)\to 2^{\frac {2}{n-2}} ((n-2) (a x-c_1)){}^{-\frac {2}{n-2}} \\ y(x)\to 0^{\frac {1}{n}} \\ \end{align*}