6.13 problem 13

Internal problem ID [4311]

Book: Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley. 2006
Section: Chapter 8, Ordinary differential equations. Section 6. SECOND-ORDER LINEAR EQUATIONSWITH CONSTANT COEFFICIENTS AND RIGHT-HAND SIDE NOT ZERO. page 422
Problem number: 13.
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*}

Solution by Maple

Time used: 0.004 (sec). Leaf size: 18

dsolve(diff(y(x),x$2)-2*diff(y(x),x)+y(x)=2*cos(x),y(x), singsol=all)
 

\[ y \relax (x ) = c_{2} {\mathrm e}^{x}+{\mathrm e}^{x} c_{1} x -\sin \relax (x ) \]

Solution by Mathematica

Time used: 0.034 (sec). Leaf size: 21

DSolve[y''[x]-2*y'[x]+y[x]==2*Cos[x],y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\sin (x)+e^x (c_2 x+c_1) \\ \end{align*}