Internal problem ID [6579]
Book: First order enumerated odes
Section: section 1
Problem number: 16.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_linear, class A]]
Solve \begin {gather*} \boxed {c y^{\prime }-x a -b y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 28
dsolve(c*diff(y(x),x)=a*x+b*y(x),y(x), singsol=all)
\[ y \relax (x ) = -\frac {a x}{b}-\frac {a c}{b^{2}}+{\mathrm e}^{\frac {b x}{c}} c_{1} \]
✓ Solution by Mathematica
Time used: 0.056 (sec). Leaf size: 28
DSolve[c*y'[x]==a*x+b*y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {a (b x+c)}{b^2}+c_1 e^{\frac {b x}{c}} \\ \end{align*}