39.5.6 problem Problem 24.28

Internal problem ID [6548]
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 24.28
Date solved : Monday, January 27, 2025 at 02:12:06 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

Using Laplace method With initial conditions

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

✓ Solution by Maple

Time used: 0.164 (sec). Leaf size: 20

dsolve([diff(y(x),x$2)-y(x)=exp(x),y(0) = 1, D(y)(0) = 0],y(x), singsol=all)
 

\[ y = \frac {3 \,{\mathrm e}^{-x}}{4}+\frac {{\mathrm e}^{x} \left (2 x +1\right )}{4} \]

✓ Solution by Mathematica

Time used: 0.019 (sec). Leaf size: 27

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

\[ y(x)\to \frac {1}{4} e^{-x} \left (e^{2 x} (2 x+1)+3\right ) \]