Internal problem ID [2529]
Book: Elementary Differential equations, Chaundy, 1969
Section: Exercises 3, page 60
Problem number: 2(d).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {y^{\prime } x -n y-x^{n}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 12
dsolve(x*diff(y(x),x)-n*y(x)=x^n,y(x), singsol=all)
\[ y \relax (x ) = \left (\ln \relax (x )+c_{1}\right ) x^{n} \]
✓ Solution by Mathematica
Time used: 0.045 (sec). Leaf size: 14
DSolve[x*y'[x]-n*y[x]==x^n,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x^n (\log (x)+c_1) \\ \end{align*}