75.18.23 problem 612

Internal problem ID [17111]
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 ODEs). Section 15.3 Nonhomogeneous linear equations with constant coefficients. Initial value problem. Exercises page 140
Problem number : 612
Date solved : Tuesday, January 28, 2025 at 09:53:15 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-2 y^{\prime }+y&=4 \,{\mathrm e}^{-x} \end{align*}

With initial conditions

\begin{align*} y \left (\infty \right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.349 (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)
 

\[ y = -\operatorname {signum}\left ({\mathrm e}^{x} c_{1} \right ) \infty \]

✓ Solution by Mathematica

Time used: 0.033 (sec). Leaf size: 10

DSolve[{D[y[x],{x,2}]-2*D[y[x],x]+y[x]==4*Exp[-x],{y[Infinity]==0}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-x} \]