82.33.18 problem Ex. 18

Internal problem ID [18911]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter VI. Linear equations with constant coefficients. Examples on chapter VI, page 80
Problem number : Ex. 18
Date solved : Tuesday, January 28, 2025 at 12:34:15 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 43

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

\[ y \left (x \right ) = c_{2} {\mathrm e}^{-\frac {x}{2}} \sin \left (\frac {\sqrt {3}\, x}{2}\right )+{\mathrm e}^{-\frac {x}{2}} \cos \left (\frac {\sqrt {3}\, x}{2}\right ) c_{1} -\frac {3 \sin \left (2 x \right )}{13}-\frac {2 \cos \left (2 x \right )}{13} \]

✓ Solution by Mathematica

Time used: 1.724 (sec). Leaf size: 64

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

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