Internal problem ID [4548]
Book: Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section: Chapter 2. Special types of differential equations of the first kind. Lesson 12,
Miscellaneous Methods
Problem number: Exercise 12.27, page 103.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
\[ \boxed {x y^{\prime }+y a=-b \,x^{n}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 23
dsolve(x*diff(y(x),x)+a*y(x)+b*x^n=0,y(x), singsol=all)
\[ y \left (x \right ) = -\frac {x^{n} b}{a +n}+x^{-a} c_{1} \]
✓ Solution by Mathematica
Time used: 0.056 (sec). Leaf size: 25
DSolve[x*y'[x]+a*y[x]+b*x^n==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\frac {b x^n}{a+n}+c_1 x^{-a} \]