Internal problem ID [4544]
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).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-2 y^{\prime }+y-2 \cos \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: 0.009 (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)
\[ y \relax (x ) = {\mathrm e}^{x}-\sin \relax (x ) \]
✓ Solution by Mathematica
Time used: 0.034 (sec). Leaf size: 13
DSolve[{y''[x]-2*y'[x]+y[x]==2*Cos[x],{y[0]==1,y'[0]==0}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^x-\sin (x) \\ \end{align*}