Internal problem ID [4029]
Book: Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section: Chapter 2. Special types of differential equations of the first kind. Lesson 12, Miscellaneous
Methods
Problem number: Exercise 12.16, page 103.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_linear, class A]]
Solve \begin {gather*} \boxed {y^{\prime }+a y-k \,{\mathrm e}^{b x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 25
dsolve(diff(y(x),x)+a*y(x)=k*exp(b*x),y(x), singsol=all)
\[ y \relax (x ) = \left (\frac {k \,{\mathrm e}^{x \left (a +b \right )}}{a +b}+c_{1}\right ) {\mathrm e}^{-a x} \]
✓ Solution by Mathematica
Time used: 0.078 (sec). Leaf size: 33
DSolve[y'[x]+a*y[x]==k*Exp[b*x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {e^{-a x} \left (k e^{x (a+b)}+c_1 (a+b)\right )}{a+b} \\ \end{align*}