Internal problem ID [4546]
Book: Basic Training in Mathematics. By R. Shankar. Plenum Press. NY. 1995
Section: Chapter 10, Differential equations. Section 10.2, ODEs with constant Coefficients. page
307
Problem number: 10.2.11 (iv).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-y-\cosh \relax (x )=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 1, y^{\prime }\relax (0) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 23
dsolve([diff(y(x),x$2)-y(x)=cosh(x),y(0) = 1, D(y)(0) = 0],y(x), singsol=all)
\[ y \relax (x ) = \frac {\left (2-x \right ) {\mathrm e}^{-x}}{4}+\frac {{\mathrm e}^{x} \left (x +2\right )}{4} \]
✓ Solution by Mathematica
Time used: 0.035 (sec). Leaf size: 15
DSolve[{y''[x]-y[x]==Cosh[x],{y[0]==1,y'[0]==0}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} x \sinh (x)+\cosh (x) \\ \end{align*}