82.12.34 problem Ex. 37

Internal problem ID [18799]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter II. Equations of the first order and of the first degree. Examples on chapter II at page 29
Problem number : Ex. 37
Date solved : Tuesday, January 28, 2025 at 12:18:30 PM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 15

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

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

✓ Solution by Mathematica

Time used: 0.068 (sec). Leaf size: 17

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

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