69.18.25 problem 614

Internal problem ID [18400]
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 : 614
Date solved : Thursday, October 02, 2025 at 03:11:24 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-y^{\prime }-5 y&=1 \end{align*}

With initial conditions

\begin{align*} y \left (\infty \right )&=-{\frac {1}{5}} \\ \end{align*}

✓ Maple. Time used: 0.164 (sec). Leaf size: 19

ode:=diff(diff(y(x),x),x)-diff(y(x),x)-5*y(x) = 1; 
ic:=[y(infinity) = -1/5]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = -\operatorname {signum}\left (c_2 \,{\mathrm e}^{-\frac {\left (-1+\sqrt {21}\right ) x}{2}}\right ) \infty \]

✓ Mathematica. Time used: 0.037 (sec). Leaf size: 26

ode=D[y[x],{x,2}]-D[y[x],x]-5*y[x]==1; 
ic={y[Infinity]==-1/5}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -\frac {1}{5}+c_1 e^{-\frac {1}{2} \left (\sqrt {21}-1\right ) x} \end{align*}

✓ Sympy. Time used: 0.121 (sec). Leaf size: 19

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-5*y(x) - Derivative(y(x), x) + Derivative(y(x), (x, 2)) - 1,0) 
ics = {y(oo): -1/5} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} e^{\frac {x \left (1 - \sqrt {21}\right )}{2}} - \frac {1}{5} \]