Internal problem ID [3129]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 14
Problem number: 381.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {y^{\prime } x^{n}-a -b \,x^{n -1} y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.001 (sec). Leaf size: 26
dsolve(x^n*diff(y(x),x) = a+b*x^(n-1)*y(x),y(x), singsol=all)
\[ y \relax (x ) = -\frac {a \,x^{-n +1}}{n +b -1}+x^{b} c_{1} \]
✓ Solution by Mathematica
Time used: 0.118 (sec). Leaf size: 28
DSolve[x^n y'[x]==a+b x^(n-1) y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {a x^{1-n}}{b+n-1}+c_1 x^b \\ \end{align*}