28.2.31 problem 31

Internal problem ID [4474]
Book : Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section : Chapter 4. Linear Differential Equations. Page 183
Problem number : 31
Date solved : Monday, January 27, 2025 at 09:19:12 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+3 y^{\prime }+5 y&=5 \,{\mathrm e}^{-x} \sin \left (2 x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 48

dsolve(diff(y(x),x$2)+3*diff(y(x),x)+5*y(x)=5*exp(-x)*sin(2*x),y(x), singsol=all)
 

\[ y \left (x \right ) = {\mathrm e}^{-\frac {3 x}{2}} \cos \left (\frac {\sqrt {11}\, x}{2}\right ) c_{1} +{\mathrm e}^{-\frac {3 x}{2}} \sin \left (\frac {\sqrt {11}\, x}{2}\right ) c_{2} -2 \,{\mathrm e}^{-x} \left (\cos \left (2 x \right )+\frac {\sin \left (2 x \right )}{2}\right ) \]

✓ Solution by Mathematica

Time used: 0.036 (sec). Leaf size: 62

DSolve[D[y[x],{x,2}]+3*D[y[x],x]+5*y[x]==5*Exp[-x]*Sin[2*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-3 x/2} \left (-e^{x/2} (\sin (2 x)+2 \cos (2 x))+c_2 \cos \left (\frac {\sqrt {11} x}{2}\right )+c_1 \sin \left (\frac {\sqrt {11} x}{2}\right )\right ) \]