Internal problem ID [2765]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 1
Problem number: 10.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime }-a \,x^{n} y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.001 (sec). Leaf size: 19
dsolve(diff(y(x),x) = a*x^n*y(x),y(x), singsol=all)
\[ y \relax (x ) = c_{1} {\mathrm e}^{\frac {x^{n +1} a}{n +1}} \]
✓ Solution by Mathematica
Time used: 0.054 (sec). Leaf size: 27
DSolve[y'[x]==a*x^n*y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 e^{\frac {a x^{n+1}}{n+1}} \\ y(x)\to 0 \\ \end{align*}