71.13.4 problem 4

Internal problem ID [14524]
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 : 4
Date solved : Tuesday, January 28, 2025 at 06:42:57 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: 9.707 (sec). Leaf size: 30

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

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

✓ Solution by Mathematica

Time used: 0.017 (sec). Leaf size: 30

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

\[ y(x)\to -\frac {1}{9} \sin (3 x)+c_1 e^{3 x}+c_2 e^{-3 x} \]