Internal problem ID [3257]
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]]
\[ \boxed {y^{\prime \prime }+4 y=\sinh \left (x \right ) \sin \left (2 x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 49
dsolve(diff(y(x),x$2)+4*y(x)=sinh(x)*sin(2*x),y(x), singsol=all)
\[ y \left (x \right ) = \sin \left (2 x \right ) c_{2} +c_{1} \cos \left (2 x \right )+\frac {\left (-4 \,{\mathrm e}^{x}-4 \,{\mathrm e}^{-x}\right ) \cos \left (2 x \right )}{34}+\frac {\sin \left (2 x \right ) \left ({\mathrm e}^{x}-{\mathrm e}^{-x}\right )}{34} \]
✓ Solution by Mathematica
Time used: 0.119 (sec). Leaf size: 46
DSolve[y''[x]+4*y[x]==Sinh[x]*Sin[2*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{34} (-(4-i) \cos ((2+i) x)-(4+i) \cosh ((1+2 i) x)+34 c_1 \cos (2 x)+34 c_2 \sin (2 x)) \]