12.1.16 problem 8(a)

Internal problem ID [1534]
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)
Date solved : Monday, January 27, 2025 at 04:59:09 AM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=a y^{\frac {a -1}{a}} \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 9

dsolve(diff(y(x),x) = a*y(x)^( (a-1)/a),y(x), singsol=all)
 

\[ y = \left (x +c_1 \right )^{a} \]

✓ Solution by Mathematica

Time used: 0.880 (sec). Leaf size: 28

DSolve[D[y[x],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*}