24.1.9 problem 2(c)

Internal problem ID [4198]
Book : Elementary Differential equations, Chaundy, 1969
Section : Exercises 3, page 60
Problem number : 2(c)
Date solved : Monday, January 27, 2025 at 08:41:53 AM
CAS classification : [_linear]

\begin{align*} x y^{\prime }+n y&=x^{n} \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 20

dsolve(x*diff(y(x),x)+n*y(x)=x^n,y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {x^{n}}{2 n}+x^{-n} c_{1} \]

✓ Solution by Mathematica

Time used: 0.049 (sec). Leaf size: 24

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

\[ y(x)\to \frac {x^n}{2 n}+c_1 x^{-n} \]