7.11.32 problem 33

Internal problem ID [353]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 2. Linear Equations of Higher Order. Section 2.5 (Nonhomogeneous equations and undetermined coefficients). Problems at page 161
Problem number : 33
Date solved : Wednesday, February 05, 2025 at 03:24:23 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

With initial conditions

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

✓ Solution by Maple

Time used: 0.023 (sec). Leaf size: 21

dsolve([diff(y(x),x$2)+9*y(x)=sin(2*x),y(0) = 1, D(y)(0) = 0],y(x), singsol=all)
 

\[ y = -\frac {2 \sin \left (3 x \right )}{15}+\cos \left (3 x \right )+\frac {\sin \left (2 x \right )}{5} \]

✓ Solution by Mathematica

Time used: 0.089 (sec). Leaf size: 26

DSolve[{D[y[x],{x,2}]+9*y[x]==Sin[2*x],{y[0]==1,Derivative[1][y][0] ==0}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{5} \sin (2 x)-\frac {2}{15} \sin (3 x)+\cos (3 x) \]