23.2.13 problem 6(b)

Internal problem ID [4130]
Book : Theory and solutions of Ordinary Differential equations, Donald Greenspan, 1960
Section : Chapter 3. Linear differential equations of second order. Exercises at page 31
Problem number : 6(b)
Date solved : Sunday, March 30, 2025 at 02:40:35 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 18

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

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

✓ Mathematica. Time used: 0.028 (sec). Leaf size: 57

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

\[ y(x)\to -x^2+2 x+c_2 e^{-x/2} \cos \left (\frac {\sqrt {7} x}{2}\right )+c_1 e^{-x/2} \sin \left (\frac {\sqrt {7} x}{2}\right )+1 \]

✓ Sympy. Time used: 0.133 (sec). Leaf size: 17

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

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