6.1 problem 147

Internal problem ID [2895]

Book: Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section: Various 6
Problem number: 147.
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [_linear]

Solve \begin {gather*} \boxed {y^{\prime } x -x^{m}-y=0} \end {gather*}

Solution by Maple

Time used: 0.0 (sec). Leaf size: 17

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

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

Solution by Mathematica

Time used: 0.044 (sec). Leaf size: 19

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

\begin{align*} y(x)\to \frac {x^m}{m-1}+c_1 x \\ \end{align*}