Internal problem ID [15381]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Chapter 2 (Higher order ODE’s). Section 15.3 Nonhomogeneous linear equations with
constant coefficients. Initial value problem. Exercises page 140
Problem number: 612.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }-2 y^{\prime }+y=4 \,{\mathrm e}^{-x}} \] With initial conditions \begin {align*} [y \left (\infty \right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 12
dsolve([diff(y(x),x$2)-2*diff(y(x),x)+y(x)=4*exp(-x),y(infinity) = 0],y(x), singsol=all)
\[ y \left (x \right ) = -\operatorname {signum}\left (c_{1} {\mathrm e}^{x}\right ) \infty \]
✓ Solution by Mathematica
Time used: 0.053 (sec). Leaf size: 10
DSolve[{y''[x]-2*y'[x]+y[x]==4*Exp[-x],{y[Infinity]==0}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{-x} \]