Internal problem ID [4122]
Book: Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section: Chapter 4. Higher order linear differential equations. Lesson 21. Undetermined
Coefficients
Problem number: Exercise 21.33, page 231.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-3 y^{\prime }+2 y-{\mathrm e}^{-x}=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 1, y^{\prime }\relax (0) = -1] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 19
dsolve([diff(y(x),x$2)-3*diff(y(x),x)+2*y(x)=exp(-x),y(0) = 1, D(y)(0) = -1],y(x), singsol=all)
\[ y \relax (x ) = -\frac {5 \,{\mathrm e}^{2 x}}{3}+\frac {5 \,{\mathrm e}^{x}}{2}+\frac {{\mathrm e}^{-x}}{6} \]
✓ Solution by Mathematica
Time used: 0.016 (sec). Leaf size: 30
DSolve[{y''[x]-3*y'[x]+2*y[x]==Exp[-x],{y[0]==1,y'[0]==-1}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{3} (7 \sinh (x)-5 \sinh (2 x)+8 \cosh (x)-5 \cosh (2 x)) \\ \end{align*}