14.2 problem 8

Internal problem ID [12800]

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.
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [[_linear, `class A`]]

\[ \boxed {y^{\prime }+y={\mathrm e}^{x}} \] With initial conditions \begin {align*} \left [y \left (0\right ) = {\frac {5}{2}}\right ] \end {align*}

✓ Solution by Maple

Time used: 5.813 (sec). Leaf size: 13

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

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

✓ Solution by Mathematica

Time used: 0.066 (sec). Leaf size: 20

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

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