Internal problem ID [225]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 5.5, Nonhomogeneous equations and undetermined coefficients Page 351
Problem number: 7.
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 )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 69
dsolve(diff(y(x),x$2)-4*y(x)=sinh(x),y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{-2 x} c_{2}+c_{1} {\mathrm e}^{2 x}+\frac {\left (3 \cosh \relax (x )+3 \sinh \relax (x )-\cosh \left (3 x \right )-\sinh \left (3 x \right )\right ) {\mathrm e}^{-2 x}}{24}-\frac {{\mathrm e}^{2 x} \left (\cosh \relax (x )-\sinh \relax (x )-\frac {\cosh \left (3 x \right )}{3}+\frac {\sinh \left (3 x \right )}{3}\right )}{8} \]
✓ Solution by Mathematica
Time used: 0.02 (sec). Leaf size: 38
DSolve[y''[x]-4*y[x]==Sinh[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{6} e^{-2 x} \left (e^x-e^{3 x}+6 c_1 e^{4 x}+6 c_2\right ) \\ \end{align*}