32.6.27 problem Exercise 12.27, page 103

Internal problem ID [5892]
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
Date solved : Monday, January 27, 2025 at 01:24:57 PM
CAS classification : [_linear]

\begin{align*} x y^{\prime }+a y+b \,x^{n}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.002 (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: 0.074 (sec). Leaf size: 25

DSolve[x*D[y[x],x]+a*y[x]+b*x^n==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -\frac {b x^n}{a+n}+c_1 x^{-a} \]