Internal problem ID [7582]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 2.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_linear, `class A`]]
\[ \boxed {y^{\prime }+a y-c \,{\mathrm e}^{x b}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 25
dsolve(diff(y(x),x) + a*y(x) - c*exp(b*x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \left (\frac {c \,{\mathrm e}^{x \left (a +b \right )}}{a +b}+c_{1} \right ) {\mathrm e}^{-a x} \]
✓ Solution by Mathematica
Time used: 0.07 (sec). Leaf size: 33
DSolve[y'[x]+ a*y[x] - c*Exp[b*x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {e^{-a x} \left (c e^{x (a+b)}+c_1 (a+b)\right )}{a+b} \\ \end{align*}