Internal problem ID [2977]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 8
Problem number: 229.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {\left (x +a \right ) y^{\prime }-b x -y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 24
dsolve((a+x)*diff(y(x),x) = b*x+y(x),y(x), singsol=all)
\[ y \relax (x ) = \left (b \ln \left (a +x \right )+\frac {b a}{a +x}+c_{1}\right ) \left (a +x \right ) \]
✓ Solution by Mathematica
Time used: 0.037 (sec). Leaf size: 24
DSolve[(a+x) y'[x]==b x+ y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to b (a+x) \log (a+x)+a b+c_1 (a+x) \\ \end{align*}