66.2.6 problem Problem 6

Internal problem ID [13905]
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 6
Date solved : Tuesday, January 28, 2025 at 06:08:09 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 23

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

\[ y = \sin \left (x \right ) c_{2} +\cos \left (x \right ) c_{1} +\frac {{\mathrm e}^{x}}{4}+\frac {{\mathrm e}^{-x}}{4} \]

✓ Solution by Mathematica

Time used: 0.033 (sec). Leaf size: 22

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

\[ y(x)\to \frac {\cosh (x)}{2}+c_1 \cos (x)+c_2 \sin (x) \]