Internal problem ID [10839]
Book: Differential equations and the calculus of variations by L. ElSGOLTS. MIR PUBLISHERS,
MOSCOW, Third printing 1977.
Section: Chapter 2, DIFFERENTIAL EQUATIONS OF THE SECOND ORDER AND HIGHER.
Problems page 172
Problem number: Problem 33.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+2 y^{\prime }+y-\sinh \left (x \right )=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 38
dsolve(diff(y(x),x$2)+2*diff(y(x),x)+y(x)=sinh(x),y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{-x} c_{2} +x \,{\mathrm e}^{-x} c_{1} +\frac {\left (-2 x^{2}+2 x +1\right ) {\mathrm e}^{-x}}{8}+\frac {{\mathrm e}^{x}}{8} \]
✓ Solution by Mathematica
Time used: 0.017 (sec). Leaf size: 34
DSolve[y''[x]+2*y'[x]+y[x]==Sinh[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{8} e^{-x} \left (-2 x^2+e^{2 x}+8 c_2 x+8 c_1\right ) \\ \end{align*}