6.7 problem 153

Internal problem ID [2901]

Book: Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section: Various 6
Problem number: 153.
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [_linear]

Solve \begin {gather*} \boxed {y^{\prime } x -1-x -a y=0} \end {gather*}

Solution by Maple

Time used: 0.003 (sec). Leaf size: 31

dsolve(x*diff(y(x),x) = 1+x+a*y(x),y(x), singsol=all)
 

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

Solution by Mathematica

Time used: 0.078 (sec). Leaf size: 25

DSolve[x y'[x]==1+x+a y[x],y[x],x,IncludeSingularSolutions -> True]
 

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