89.22.13 problem 13

Internal problem ID [24801]
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. Exercises at page 161
Problem number : 13
Date solved : Thursday, October 02, 2025 at 10:48:08 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=6 x^{2}-6 x -11 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 24

ode:=diff(diff(y(x),x),x)-3*diff(y(x),x)+2*y(x) = 6*x^2-6*x-11; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {1}{2}+3 x^{2}+6 x +{\mathrm e}^{2 x} c_1 +{\mathrm e}^{x} c_2 \]

✓ Mathematica. Time used: 0.009 (sec). Leaf size: 31

ode=D[y[x],{x,2}]-3*D[y[x],{x,1}]+2*y[x]==6*x^2-6*x-11; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to 3 x^2+6 x+c_1 e^x+c_2 e^{2 x}+\frac {1}{2} \end{align*}

✓ Sympy. Time used: 0.057 (sec). Leaf size: 24

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-6*x**2 + 6*x + 2*y(x) - 2*Derivative(y(x), (x, 2)) + 11,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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