66.2.24 problem Problem 33

Internal problem ID [13923]
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
Date solved : Tuesday, January 28, 2025 at 06:08:44 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+2 y^{\prime }+y&=\sinh \left (x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 32

dsolve(diff(y(x),x$2)+2*diff(y(x),x)+y(x)=sinh(x),y(x), singsol=all)
 

\[ y = \frac {\left (-2 x^{2}+\left (8 c_{1} +2\right ) x +8 c_{2} +1\right ) {\mathrm e}^{-x}}{8}+\frac {{\mathrm e}^{x}}{8} \]

✓ Solution by Mathematica

Time used: 0.055 (sec). Leaf size: 34

DSolve[D[y[x],{x,2}]+2*D[y[x],x]+y[x]==Sinh[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{8} e^{-x} \left (-2 x^2+e^{2 x}+8 c_2 x+8 c_1\right ) \]