28.2.43 problem 43

Internal problem ID [4486]
Book : Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section : Chapter 4. Linear Differential Equations. Page 183
Problem number : 43
Date solved : Monday, January 27, 2025 at 09:21:09 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+2 y^{\prime }+2 y&=5 \cos \left (x \right )+10 \sin \left (2 x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 39

dsolve(diff(y(x),x$2)+2*diff(y(x),x)+2*y(x)=5*cos(x)+10*sin(2*x),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.312 (sec). Leaf size: 42

DSolve[D[y[x],{x,2}]+2*D[y[x],x]+2*y[x]==5*Cos[x]+10*Sin[2*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -2 \cos (2 x)+\left (2+c_1 e^{-x}\right ) \sin (x)+\cos (x) \left (-2 \sin (x)+c_2 e^{-x}+1\right ) \]