71.14.7 problem 13

Internal problem ID [14541]
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 : 13
Date solved : Tuesday, January 28, 2025 at 06:43:09 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-2 y^{\prime }+y&=2 \sin \left (x \right ) \end{align*}

Using Laplace method With initial conditions

\begin{align*} y \left (0\right )&=-2\\ y^{\prime }\left (0\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 8.342 (sec). Leaf size: 15

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

\[ y = \left (3 x -3\right ) {\mathrm e}^{x}+\cos \left (x \right ) \]

✓ Solution by Mathematica

Time used: 0.015 (sec). Leaf size: 16

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

\[ y(x)\to 3 e^x (x-1)+\cos (x) \]