28.2.17 problem 17

Internal problem ID [4460]
Book : Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section : Chapter 4. Linear Differential Equations. Page 183
Problem number : 17
Date solved : Monday, January 27, 2025 at 09:18:43 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.003 (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)
 

\[ y \left (x \right ) = \frac {\left (\left (-x +4 c_{1} \right ) \cos \left (x \right )+4 c_{2} \sin \left (x \right )\right ) {\mathrm e}^{-x}}{4}-\frac {{\mathrm e}^{x} \left (-\sin \left (x \right )+\cos \left (x \right )\right )}{16} \]

✓ Solution by Mathematica

Time used: 0.184 (sec). Leaf size: 47

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

\[ y(x)\to \frac {1}{16} e^{-x} \left (\left (e^{2 x}+2+16 c_1\right ) \sin (x)-\left (e^{2 x}+4 (x-4 c_2)\right ) \cos (x)\right ) \]