69.16.1 problem 474

Internal problem ID [18261]
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 : 474
Date solved : Thursday, October 02, 2025 at 03:09:52 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+3 y^{\prime }&=3 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 14

ode:=diff(diff(y(x),x),x)+3*diff(y(x),x) = 3; 
dsolve(ode,y(x), singsol=all);
 

\[ y = -\frac {{\mathrm e}^{-3 x} c_1}{3}+x +c_2 \]

✓ Mathematica. Time used: 0.009 (sec). Leaf size: 20

ode=D[y[x],{x,2}]+3*D[y[x],x]==3; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to x-\frac {1}{3} c_1 e^{-3 x}+c_2 \end{align*}

✓ Sympy. Time used: 0.080 (sec). Leaf size: 12

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(3*Derivative(y(x), x) + Derivative(y(x), (x, 2)) - 3,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} + C_{2} e^{- 3 x} + x \]