39.5.8 problem Problem 24.30

Internal problem ID [6550]
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 24.30
Date solved : Monday, January 27, 2025 at 02:12:08 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 )&=2 \end{align*}

✓ Solution by Maple

Time used: 0.166 (sec). Leaf size: 14

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

\[ y = \frac {5 \sin \left (x \right )}{2}-\frac {\cos \left (x \right ) x}{2} \]

✓ Solution by Mathematica

Time used: 0.035 (sec). Leaf size: 19

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

\[ y(x)\to \frac {1}{2} (5 \sin (x)-x \cos (x)) \]