Internal problem ID [3270]
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`]]
\[ \boxed {y^{\prime }-c y=a +b \,{\mathrm e}^{k x}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 39
dsolve(diff(y(x),x) = a+b*exp(k*x)+c*y(x),y(x), singsol=all)
\[ y \left (x \right ) = -\frac {a}{c}+\frac {b \,{\mathrm e}^{-x \left (c -k \right )+c x}}{-c +k}+{\mathrm e}^{c x} c_{1} \]
✓ Solution by Mathematica
Time used: 0.166 (sec). Leaf size: 47
DSolve[y'[x]==a+b*Exp[k*x]+c*y[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {a (k-c)-b c e^{k x}+c c_1 (c-k) e^{c x}}{c (c-k)} \]