64.5.31 problem 31

Internal problem ID [13344]
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
Date solved : Tuesday, January 28, 2025 at 05:31:14 AM
CAS classification : [[_linear, `class A`]]

\begin{align*} a y^{\prime }+b y&=k \,{\mathrm e}^{-\lambda x} \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 49

dsolve(a*diff(y(x),x)+b*y(x)=k*exp(-lambda*x),y(x), singsol=all)
 

\[ y = \frac {{\mathrm e}^{-\frac {b x}{a}} \left (-k \,{\mathrm e}^{-\frac {x \left (a \lambda -b \right )}{a}}+c_{1} \left (a \lambda -b \right )\right )}{a \lambda -b} \]

✓ Solution by Mathematica

Time used: 0.093 (sec). Leaf size: 44

DSolve[a*D[y[x],x]+b*y[x]==k*Exp[\[Lambda]*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {e^{-\frac {b x}{a}} \left (k e^{x \left (\frac {b}{a}+\lambda \right )}+c_1 (a \lambda +b)\right )}{a \lambda +b} \]