28.2.13 problem 13

Internal problem ID [4456]
Book : Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section : Chapter 4. Linear Differential Equations. Page 183
Problem number : 13
Date solved : Monday, January 27, 2025 at 09:17:52 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+6 y^{\prime }+10 y&=3 x \,{\mathrm e}^{-3 x}-2 \,{\mathrm e}^{3 x} \cos \left (x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 35

dsolve(diff(y(x),x$2)+6*diff(y(x),x)+10*y(x)=3*x*exp(-3*x)-2*exp(3*x)*cos(x),y(x), singsol=all)
 

\[ y \left (x \right ) = \left (\cos \left (x \right ) c_{1} +c_{2} \sin \left (x \right )+3 x \right ) {\mathrm e}^{-3 x}-\frac {\left (\cos \left (x \right )+\frac {\sin \left (x \right )}{3}\right ) {\mathrm e}^{3 x}}{20} \]

✓ Solution by Mathematica

Time used: 0.397 (sec). Leaf size: 46

DSolve[D[y[x],{x,2}]+6*D[y[x],x]+10*y[x]==3*x*Exp[-3*x]-2*Exp[3*x]*Cos[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{60} e^{-3 x} \left (180 x-3 \left (e^{6 x}-20 c_2\right ) \cos (x)-\left (e^{6 x}-60 c_1\right ) \sin (x)\right ) \]