Internal problem ID [2761]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 1
Problem number: 6.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_linear, class A]]
Solve \begin {gather*} \boxed {y^{\prime }-a -b \,{\mathrm e}^{k x}-c y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 39
dsolve(diff(y(x),x) = a+b*exp(k*x)+c*y(x),y(x), singsol=all)
\[ y \relax (x ) = -\frac {a}{c}+\frac {b \,{\mathrm e}^{c x -x \left (c -k \right )}}{-c +k}+{\mathrm e}^{c x} c_{1} \]
✓ Solution by Mathematica
Time used: 0.128 (sec). Leaf size: 34
DSolve[y'[x]==a+b*Exp[k*x]+c*y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {a}{c}+\frac {b e^{k x}}{k-c}+c_1 e^{c x} \\ \end{align*}