Internal problem ID [4645]
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]]
\[ \boxed {y^{\prime \prime }-3 y^{\prime }+2 y=\cos \left ({\mathrm e}^{-x}\right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 24
dsolve(diff(y(x),x$2)-3*diff(y(x),x)+2*y(x)=cos(exp(-x)),y(x), singsol=all)
\[ y \left (x \right ) = \left (-{\mathrm e}^{x} \cos \left ({\mathrm e}^{-x}\right )+\left (c_{1} -1\right ) {\mathrm e}^{x}+c_{2} \right ) {\mathrm e}^{x} \]
✓ Solution by Mathematica
Time used: 0.082 (sec). Leaf size: 29
DSolve[y''[x]-3*y'[x]+2*y[x]==Cos[Exp[-x]],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^x \left (-e^x \cos \left (e^{-x}\right )+c_2 e^x+c_1\right ) \]