40.9.7 problem 17

Internal problem ID [6717]
Book : Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres. McGraw Hill 1952
Section : Chapter 14. Linear equations with constant coefficients. Supplemetary problems. Page 92
Problem number : 17
Date solved : Wednesday, March 05, 2025 at 02:40:01 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: 25

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);
 

\[ y = \left ({\mathrm e}^{3 x} c_2 +{\mathrm e}^{2 x} x^{2}+c_1 \right ) {\mathrm e}^{-2 x} \]

✓ Mathematica. Time used: 0.015 (sec). Leaf size: 23

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]
 

\[ y(x)\to x^2+c_1 e^{-2 x}+c_2 e^x \]

✓ Sympy. Time used: 0.195 (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)
 

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