Internal problem ID [4137]
Book: Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section: Chapter 4. Higher order linear differential equations. Lesson 22. Variation of Parameters
Problem number: Exercise 22.15, page 240.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-3 y^{\prime }+2 y-\cos \left ({\mathrm e}^{-x}\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 26
dsolve(diff(y(x),x$2)-3*diff(y(x),x)+2*y(x)=cos(exp(-x)),y(x), singsol=all)
\[ y \relax (x ) = \left (c_{1} {\mathrm e}^{x}-{\mathrm e}^{x}-{\mathrm e}^{x} \cos \left ({\mathrm e}^{-x}\right )+c_{2}\right ) {\mathrm e}^{x} \]
✓ Solution by Mathematica
Time used: 0.06 (sec). Leaf size: 27
DSolve[y''[x]-3*y'[x]+2*y[x]==Cos[Exp[-x]],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^x \left (e^x \left (-\cos \left (e^{-x}\right )+c_2\right )+c_1\right ) \\ \end{align*}