39.5.5 problem Problem 24.27

Internal problem ID [6547]
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 24.27
Date solved : Monday, January 27, 2025 at 02:12:06 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-y&=\sin \left (x \right ) \end{align*}

Using Laplace method With initial conditions

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

✓ Solution by Maple

Time used: 0.165 (sec). Leaf size: 13

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

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

✓ Solution by Mathematica

Time used: 0.032 (sec). Leaf size: 26

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

\[ y(x)\to \frac {1}{4} \left (-e^{-x}+5 e^x-2 \sin (x)\right ) \]