37.1.10 problem 10.2.11 (iv)

Internal problem ID [6397]
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)
Date solved : Monday, January 27, 2025 at 02:00:26 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

With initial conditions

\begin{align*} y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.013 (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)
 

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

✓ Solution by Mathematica

Time used: 0.040 (sec). Leaf size: 28

DSolve[{D[y[x],{x,2}]-y[x]==Cosh[x],{y[0]==1,Derivative[1][y][0] ==0}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{4} e^{-x} \left (-x+e^{2 x} (x+2)+2\right ) \]