29.26.27 problem 763

Internal problem ID [5348]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 26
Problem number : 763
Date solved : Monday, January 27, 2025 at 11:16:44 AM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.148 (sec). Leaf size: 72

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

\begin{align*} y \left (x \right ) &= 4^{\frac {1}{n -2}} \left (-\frac {1}{a \left (-c_{1} +x \right ) \left (n -2\right )}\right )^{\frac {2}{n -2}} \\ y \left (x \right ) &= 4^{\frac {1}{n -2}} \left (\frac {1}{a \left (-c_{1} +x \right ) \left (n -2\right )}\right )^{\frac {2}{n -2}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 1.796 (sec). Leaf size: 77

DSolve[(D[y[x],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*}