71.13.5 problem 5

Internal problem ID [14525]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 5. The Laplace Transform Method. Exercises 5.2, page 248
Problem number : 5
Date solved : Tuesday, January 28, 2025 at 06:42:58 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+9 y&=2 \sin \left (3 x \right ) \end{align*}

Using Laplace method

✓ Solution by Maple

Time used: 9.641 (sec). Leaf size: 29

dsolve(diff(y(x),x$2)+9*y(x)=2*sin(3*x),y(x), singsol=all)
 

\[ y = -\frac {\cos \left (3 x \right ) \left (x -3 y \left (0\right )\right )}{3}+\frac {\sin \left (3 x \right ) \left (1+3 y^{\prime }\left (0\right )\right )}{9} \]

✓ Solution by Mathematica

Time used: 0.036 (sec). Leaf size: 64

DSolve[D[y[x],{x,2}]+9*y[x]==2*Sin[3*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \sin (3 x) \int _1^x\frac {1}{3} \sin (6 K[2])dK[2]+\cos (3 x) \int _1^x-\frac {2}{3} \sin ^2(3 K[1])dK[1]+c_1 \cos (3 x)+c_2 \sin (3 x) \]