19.2.13 problem 13

Internal problem ID [3542]
Book : Differential equations and linear algebra, Stephen W. Goode, second edition, 2000
Section : 1.6, page 50
Problem number : 13
Date solved : Monday, January 27, 2025 at 07:41:13 AM
CAS classification : [[_linear, `class A`]]

\begin{align*} y^{\prime }+\alpha y&={\mathrm e}^{\beta x} \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 27

dsolve(diff(y(x),x)+alpha*y(x)=exp(beta*x),y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {\left ({\mathrm e}^{x \left (\alpha +\beta \right )}+c_{1} \left (\alpha +\beta \right )\right ) {\mathrm e}^{-\alpha x}}{\alpha +\beta } \]

✓ Solution by Mathematica

Time used: 0.066 (sec). Leaf size: 31

DSolve[D[y[x],x]+\[Alpha]*y[x]==Exp[\[Beta]*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {e^{\alpha (-x)} \left (e^{x (\alpha +\beta )}+c_1 (\alpha +\beta )\right )}{\alpha +\beta } \]