39.5.3 problem Problem 24.19

Internal problem ID [6545]
Book : Schaums Outline Differential Equations, 4th edition. Bronson and Costa. McGraw Hill 2014
Section : Chapter 24. Solutions of linear DE by Laplace transforms. Supplementary Problems. page 248
Problem number : Problem 24.19
Date solved : Monday, January 27, 2025 at 02:12:04 PM
CAS classification : [[_linear, `class A`]]

\begin{align*} y^{\prime }+2 y&={\mathrm e}^{x} \end{align*}

Using Laplace method With initial conditions

\begin{align*} y \left (0\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.152 (sec). Leaf size: 16

dsolve([diff(y(x),x)+2*y(x)=exp(x),y(0) = 1],y(x), singsol=all)
 

\[ y = \frac {\left ({\mathrm e}^{3 x}+2\right ) {\mathrm e}^{-2 x}}{3} \]

✓ Solution by Mathematica

Time used: 0.046 (sec). Leaf size: 21

DSolve[{D[y[x],x]+2*y[x]==Exp[x],{y[0]==1}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{3} e^{-2 x} \left (e^{3 x}+2\right ) \]