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: 44
dsolve(diff(y(x),x) = a+b*exp(k*x)+c*y(x),y(x), singsol=all)
\[ y \left (x \right ) = \frac {c_{1} c \left (c -k \right ) {\mathrm e}^{c x}-b \,{\mathrm e}^{k x} c -a \left (c -k \right )}{c \left (c -k \right )} \]
✓ 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]
\[ y(x)\to \frac {a (k-c)-b c e^{k x}+c c_1 (c-k) e^{c x}}{c (c-k)} \]