Internal problem ID [2981]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 8
Problem number: 233.
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 -c y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 28
dsolve((a+x)*diff(y(x),x) = b*x+c*y(x),y(x), singsol=all)
\[ y \relax (x ) = \left (a +x \right )^{c} c_{1}-\frac {b \left (c x +a \right )}{c \left (c -1\right )} \]
✓ Solution by Mathematica
Time used: 0.082 (sec). Leaf size: 32
DSolve[(a+x) y'[x]==b x+c y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {a b+b c x}{c-c^2}+c_1 (a+x)^c \\ \end{align*}