64.11.33 problem 33

Internal problem ID [13483]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 4, Section 4.3. The method of undetermined coefficients. Exercises page 151
Problem number : 33
Date solved : Tuesday, January 28, 2025 at 05:45:17 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-4 y^{\prime }+13 y&=8 \sin \left (3 x \right ) \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=2 \end{align*}

✓ Solution by Maple

Time used: 0.026 (sec). Leaf size: 31

dsolve([diff(y(x),x$2)-4*diff(y(x),x)+13*y(x)=8*sin(3*x),y(0) = 1, D(y)(0) = 2],y(x), singsol=all)
 

\[ y = \frac {\left (2 \,{\mathrm e}^{2 x}+3\right ) \cos \left (3 x \right )}{5}+\frac {\sin \left (3 x \right ) \left (1+{\mathrm e}^{2 x}\right )}{5} \]

✓ Solution by Mathematica

Time used: 0.023 (sec). Leaf size: 36

DSolve[{D[y[x],{x,2}]-4*D[y[x],x]+13*y[x]==8*Sin[3*x],{y[0]==1,Derivative[1][y][0] ==2}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{5} \left (\left (e^{2 x}+1\right ) \sin (3 x)+\left (2 e^{2 x}+3\right ) \cos (3 x)\right ) \]