Internal problem ID [11668]
Book: Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi.
2004.
Section: Chapter 2, section 2.3 (Linear equations). Exercises page 56
Problem number: 31.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_linear, `class A`]]
\[ \boxed {a y^{\prime }+y b=k \,{\mathrm e}^{-\lambda x}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 49
dsolve(a*diff(y(x),x)+b*y(x)=k*exp(-lambda*x),y(x), singsol=all)
\[ y \left (x \right ) = \frac {\left (-k \,{\mathrm e}^{-\frac {x \left (a \lambda -b \right )}{a}}+c_{1} \left (a \lambda -b \right )\right ) {\mathrm e}^{-\frac {b x}{a}}}{a \lambda -b} \]
✓ Solution by Mathematica
Time used: 0.087 (sec). Leaf size: 44
DSolve[a*y'[x]+b*y[x]==k*Exp[\[Lambda]*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {e^{-\frac {b x}{a}} \left (k e^{x \left (\frac {b}{a}+\lambda \right )}+c_1 (a \lambda +b)\right )}{a \lambda +b} \]