Internal problem ID [884]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 1, Introduction. Section 1.2 Page 14
Problem number: 8(a).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {y^{\prime }-a y^{\frac {a -1}{a}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 9
dsolve(diff(y(x),x) = a*y(x)^( (a-1)/a),y(x), singsol=all)
\[ y \relax (x ) = \left (c_{1}+x \right )^{a} \]
✓ Solution by Mathematica
Time used: 0.848 (sec). Leaf size: 28
DSolve[y'[x] ==a*y[x]^( (a-1)/a),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \left (x+\frac {c_1}{a}\right ){}^a \\ y(x)\to 0^{\frac {a}{a-1}} \\ \end{align*}