Internal problem ID [7675]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 94.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {x y^{\prime }+a y+b \,x^{n}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 23
dsolve(x*diff(y(x),x) +a*y(x) + b*x^n=0,y(x), singsol=all)
\[ y \relax (x ) = -\frac {b \,x^{n}}{a +n}+x^{-a} c_{1} \]
✓ Solution by Mathematica
Time used: 0.098 (sec). Leaf size: 25
DSolve[x*y'[x] +a*y[x] + b*x^n==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {b x^n}{a+n}+c_1 x^{-a} \\ \end{align*}