24.1.10 problem 2(d)

Internal problem ID [4199]
Book : Elementary Differential equations, Chaundy, 1969
Section : Exercises 3, page 60
Problem number : 2(d)
Date solved : Monday, January 27, 2025 at 08:41:55 AM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 12

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

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

✓ Solution by Mathematica

Time used: 0.046 (sec). Leaf size: 14

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

\[ y(x)\to x^n (\log (x)+c_1) \]