Internal problem ID [245]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 5.5, Nonhomogeneous equations and undetermined coefficients Page 351
Problem number: 50.
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 \left (2 x \right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 35
dsolve(diff(y(x),x$2)-4*y(x)=sinh(2*x),y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{-2 x} c_{2}+{\mathrm e}^{2 x} c_{1}+\frac {{\mathrm e}^{2 x} \left (4 x -1\right )}{32}+\frac {{\mathrm e}^{-2 x} x}{8} \]
✓ Solution by Mathematica
Time used: 0.02 (sec). Leaf size: 38
DSolve[y''[x]-4*y[x]==Sinh[2*x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{32} e^{-2 x} \left (4 x+e^{4 x} (4 x-1+32 c_1)+1+32 c_2\right ) \\ \end{align*}