89.16.41 problem 41

Internal problem ID [24691]
Book : A short course in Differential Equations. Earl D. Rainville. Second edition. 1958. Macmillan Publisher, NY. CAT 58-5010
Section : Chapter 9. Nonhomogeneous Equations: Undetermined coefficients. Exercises at page 140
Problem number : 41
Date solved : Thursday, October 02, 2025 at 10:47:08 PM
CAS classification : [[_2nd_order, _missing_y]]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 21

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

\[ y = -{\mathrm e}^{-x} c_1 -x^{2}+4 x +c_2 \]

✓ Mathematica. Time used: 0.037 (sec). Leaf size: 25

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

\begin{align*} y(x)&\to -x^2+4 x-c_1 e^{-x}+c_2 \end{align*}

✓ Sympy. Time used: 0.082 (sec). Leaf size: 17

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-4*x + Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} + C_{2} e^{- x} + 2 x^{2} - 4 x \]