8.11.21 problem 44

Internal problem ID [889]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 5.5, Nonhomogeneous equations and undetermined coefficients Page 351
Problem number : 44
Date solved : Wednesday, February 05, 2025 at 04:42:13 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 55

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

\[ y = {\mathrm e}^{-\frac {x}{2}} \sin \left (\frac {\sqrt {3}\, x}{2}\right ) c_2 +{\mathrm e}^{-\frac {x}{2}} \cos \left (\frac {\sqrt {3}\, x}{2}\right ) c_1 +\frac {15 \cos \left (4 x \right )}{482}-\frac {2 \sin \left (4 x \right )}{241}-\frac {3 \cos \left (2 x \right )}{26}+\frac {\sin \left (2 x \right )}{13} \]

✓ Solution by Mathematica

Time used: 2.127 (sec). Leaf size: 80

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

\[ y(x)\to \frac {1}{13} \sin (2 x)-\frac {2}{241} \sin (4 x)-\frac {3}{26} \cos (2 x)+\frac {15}{482} \cos (4 x)+c_2 e^{-x/2} \cos \left (\frac {\sqrt {3} x}{2}\right )+c_1 e^{-x/2} \sin \left (\frac {\sqrt {3} x}{2}\right ) \]