28.2.16 problem 16

Internal problem ID [4459]
Book : Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section : Chapter 4. Linear Differential Equations. Page 183
Problem number : 16
Date solved : Monday, January 27, 2025 at 09:18:38 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+4 y&=\sinh \left (x \right ) \sin \left (2 x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 42

dsolve(diff(y(x),x$2)+4*y(x)=sinh(x)*sin(2*x),y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {\left (34 c_{1} -4 \,{\mathrm e}^{x}-4 \,{\mathrm e}^{-x}\right ) \cos \left (2 x \right )}{34}+\left (c_{2} +\frac {{\mathrm e}^{x}}{34}-\frac {{\mathrm e}^{-x}}{34}\right ) \sin \left (2 x \right ) \]

✓ Solution by Mathematica

Time used: 0.121 (sec). Leaf size: 46

DSolve[D[y[x],{x,2}]+4*y[x]==Sinh[x]*Sin[2*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{34} (-(4-i) \cos ((2+i) x)-(4+i) \cosh ((1+2 i) x)+34 c_1 \cos (2 x)+34 c_2 \sin (2 x)) \]