Internal problem ID [2749]
Book: Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section: Chapter 4. Linear Differential Equations. Page 183
Problem number: 17.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+2 y^{\prime }+2 y-\cosh \relax (x ) \sin \relax (x )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.005 (sec). Leaf size: 41
dsolve(diff(y(x),x$2)+2*diff(y(x),x)+2*y(x)=cosh(x)*sin(x),y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{-x} \sin \relax (x ) c_{2}+{\mathrm e}^{-x} \cos \relax (x ) c_{1}-\frac {{\mathrm e}^{-x} \cos \relax (x ) x}{4}-\frac {{\mathrm e}^{x} \left (\cos \relax (x )-\sin \relax (x )\right )}{16} \]
✓ Solution by Mathematica
Time used: 0.084 (sec). Leaf size: 47
DSolve[y''[x]+2*y'[x]+2*y[x]==Cosh[x]*Sin[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{16} e^{-x} \left (\left (e^{2 x}+2+16 c_1\right ) \sin (x)-\left (e^{2 x}+4 (x-4 c_2)\right ) \cos (x)\right ) \\ \end{align*}