71.14.2 problem 8

Internal problem ID [14536]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 5. The Laplace Transform Method. Exercises 5.3, page 255
Problem number : 8
Date solved : Tuesday, January 28, 2025 at 06:43:05 AM
CAS classification : [[_linear, `class A`]]

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

Using Laplace method With initial conditions

\begin{align*} y \left (0\right )&={\frac {5}{2}} \end{align*}

✓ Solution by Maple

Time used: 9.553 (sec). Leaf size: 13

dsolve([diff(y(x),x)+y(x)=exp(x),y(0) = 5/2],y(x), singsol=all)
 

\[ y = \frac {5 \cosh \left (x \right )}{2}-\frac {3 \sinh \left (x \right )}{2} \]

✓ Solution by Mathematica

Time used: 0.039 (sec). Leaf size: 20

DSolve[{D[y[x],x]+y[x]==Exp[x],{y[0]==5/2}},y[x],x,IncludeSingularSolutions -> True]
 

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