75.16.38 problem 511

Internal problem ID [16932]
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. Trial and error method. Exercises page 132
Problem number : 511
Date solved : Thursday, March 13, 2025 at 09:00:37 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+2 y^{\prime }&=-2 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 16

ode:=diff(diff(y(x),x),x)+2*diff(y(x),x) = -2; 
dsolve(ode,y(x), singsol=all);
 

\[ y = -\frac {c_{1} {\mathrm e}^{-2 x}}{2}-x +c_{2} \]

✓ Mathematica. Time used: 0.016 (sec). Leaf size: 22

ode=D[y[x],{x,2}]+2*D[y[x],x]==-2; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to -x-\frac {1}{2} c_1 e^{-2 x}+c_2 \]

✓ Sympy. Time used: 0.145 (sec). Leaf size: 12

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

\[ y{\left (x \right )} = C_{1} + C_{2} e^{- 2 x} - x \]