Internal problem ID [3258]
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]]
\[ \boxed {y^{\prime \prime }+2 y^{\prime }+2 y=\cosh \left (x \right ) \sin \left (x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 38
dsolve(diff(y(x),x$2)+2*diff(y(x),x)+2*y(x)=cosh(x)*sin(x),y(x), singsol=all)
\[ y \left (x \right ) = \frac {\left (\left (-x +4 c_{1} \right ) \cos \left (x \right )+4 \sin \left (x \right ) c_{2} \right ) {\mathrm e}^{-x}}{4}-\frac {{\mathrm e}^{x} \left (-\sin \left (x \right )+\cos \left (x \right )\right )}{16} \]
✓ Solution by Mathematica
Time used: 0.199 (sec). Leaf size: 47
DSolve[y''[x]+2*y'[x]+2*y[x]==Cosh[x]*Sin[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{16} e^{-x} \left (\left (e^{2 x}+2+16 c_1\right ) \sin (x)-\left (e^{2 x}+4 (x-4 c_2)\right ) \cos (x)\right ) \]