32.6.16 problem Exercise 12.16, page 103

Internal problem ID [5881]
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
Date solved : Monday, January 27, 2025 at 01:23:39 PM
CAS classification : [[_linear, `class A`]]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 29

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

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

✓ Solution by Mathematica

Time used: 0.080 (sec). Leaf size: 33

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

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