Internal problem ID [2748]
Book: Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section: Chapter 4. Linear Differential Equations. Page 183
Problem number: 16.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+4 y-\sinh \relax (x ) \sin \left (2 x \right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 49
dsolve(diff(y(x),x$2)+4*y(x)=sinh(x)*sin(2*x),y(x), singsol=all)
\[ y \relax (x ) = \sin \left (2 x \right ) c_{2}+\cos \left (2 x \right ) c_{1}+\frac {\left (-4 \,{\mathrm e}^{x}-4 \,{\mathrm e}^{-x}\right ) \cos \left (2 x \right )}{34}+\frac {\sin \left (2 x \right ) \left ({\mathrm e}^{x}-{\mathrm e}^{-x}\right )}{34} \]
✓ Solution by Mathematica
Time used: 0.049 (sec). Leaf size: 38
DSolve[y''[x]+4*y[x]==Sinh[x]*Sin[2*x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {4}{17} \cos (2 x) \cosh (x)+c_1 \cos (2 x)+\frac {1}{17} \sin (2 x) (\sinh (x)+17 c_2) \\ \end{align*}