37.1.8 problem 10.2.11 (ii)

Internal problem ID [6395]
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 (ii)
Date solved : Monday, January 27, 2025 at 02:00:19 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-2 y^{\prime }+y&=2 \cos \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: 0.008 (sec). Leaf size: 11

dsolve([diff(y(x),x$2)-2*diff(y(x),x)+y(x)=2*cos(x),y(0) = 1, D(y)(0) = 0],y(x), singsol=all)
 

\[ y = {\mathrm e}^{x}-\sin \left (x \right ) \]

✓ Solution by Mathematica

Time used: 0.017 (sec). Leaf size: 13

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

\[ y(x)\to e^x-\sin (x) \]