Internal problem ID [4639]
Book: Engineering Mathematics. By K. A. Stroud. 5th edition. Industrial press Inc. NY.
2001
Section: Program 25. Second order differential equations. Further problems 25. page 1094
Problem number: 4.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+2 y^{\prime }+y-4 \sinh \relax (x )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 38
dsolve(diff(y(x),x$2)+2*diff(y(x),x)+y(x)=4*sinh(x),y(x), singsol=all)
\[ y \relax (x ) = c_{2} {\mathrm e}^{-x}+x \,{\mathrm e}^{-x} c_{1}+\frac {\left (-2 x^{2}+2 x +1\right ) {\mathrm e}^{-x}}{2}+\frac {{\mathrm e}^{x}}{2} \]
✓ Solution by Mathematica
Time used: 0.039 (sec). Leaf size: 30
DSolve[y''[x]+2*y'[x]+y[x]==4*Sinh[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {e^x}{2}+e^{-x} (x (-x+c_2)+c_1) \\ \end{align*}