29.6.1 problem 147

Internal problem ID [4747]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 6
Problem number : 147
Date solved : Monday, January 27, 2025 at 09:36:17 AM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 17

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

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

✓ Solution by Mathematica

Time used: 0.048 (sec). Leaf size: 19

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

\[ y(x)\to \frac {x^m}{m-1}+c_1 x \]