69.1.44 problem 63

Internal problem ID [14197]
Book : DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR PUBLISHERS, Moscow 1969.
Section : Chapter 8. Differential equations. Exercises page 595
Problem number : 63
Date solved : Tuesday, January 28, 2025 at 06:21:34 AM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 15

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

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

✓ Solution by Mathematica

Time used: 0.069 (sec). Leaf size: 17

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

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