89.23.24 problem 24

Internal problem ID [24828]
Book : A short course in Differential Equations. Earl D. Rainville. Second edition. 1958. Macmillan Publisher, NY. CAT 58-5010
Section : Chapter 10. Nonhomogeneous Equations: Operational methods. Miscellaneous Exercises at page 162
Problem number : 24
Date solved : Thursday, October 02, 2025 at 10:48:23 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=x^{2}-2 x \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 24

ode:=diff(diff(y(x),x),x)-3*diff(y(x),x)+2*y(x) = x^2-2*x; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {1}{4}+\frac {x}{2}+\frac {x^{2}}{2}+{\mathrm e}^{2 x} c_1 +{\mathrm e}^{x} c_2 \]

✓ Mathematica. Time used: 0.008 (sec). Leaf size: 34

ode=D[y[x],{x,2}]-3*D[y[x],{x,1}]+2*y[x]==x^2-2*x; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {1}{4} \left (2 x^2+2 x+1\right )+c_1 e^x+c_2 e^{2 x} \end{align*}

✓ Sympy. Time used: 0.120 (sec). Leaf size: 26

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

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