64.11.4 problem 4

Internal problem ID [13454]
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 : 4
Date solved : Tuesday, January 28, 2025 at 05:43:32 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+2 y^{\prime }+2 y&=10 \sin \left (4 x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 33

dsolve(diff(y(x),x$2)+2*diff(y(x),x)+2*y(x)=10*sin(4*x),y(x), singsol=all)
 

\[ y = \sin \left (x \right ) {\mathrm e}^{-x} c_{2} +{\mathrm e}^{-x} c_{1} \cos \left (x \right )-\frac {7 \sin \left (4 x \right )}{13}-\frac {4 \cos \left (4 x \right )}{13} \]

✓ Solution by Mathematica

Time used: 0.022 (sec). Leaf size: 42

DSolve[D[y[x],{x,2}]+2*D[y[x],x]+2*y[x]==10*Sin[4*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -\frac {7}{13} \sin (4 x)-\frac {4}{13} \cos (4 x)+c_2 e^{-x} \cos (x)+c_1 e^{-x} \sin (x) \]