Internal problem ID [10821]
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.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+y-\cosh \left (x \right )=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 23
dsolve(diff(y(x),x$2)+y(x)=cosh(x),y(x), singsol=all)
\[ y \left (x \right ) = c_{1} \cos \left (x \right )+c_{2} \sin \left (x \right )+\frac {{\mathrm e}^{x}}{4}+\frac {{\mathrm e}^{-x}}{4} \]
✓ Solution by Mathematica
Time used: 0.016 (sec). Leaf size: 22
DSolve[y''[x]+y[x]==Cosh[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {\cosh (x)}{2}+c_1 \cos (x)+c_2 \sin (x) \\ \end{align*}