20.6.17 problem Problem 39

Internal problem ID [3712]
Book : Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition, 2015
Section : Chapter 8, Linear differential equations of order n. Section 8.1, General Theory for Linear Differential Equations. page 502
Problem number : Problem 39
Date solved : Sunday, March 30, 2025 at 02:06:17 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+y^{\prime }-2 y&=4 x^{2}+5 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 24

ode:=diff(diff(y(x),x),x)+diff(y(x),x)-2*y(x) = 4*x^2+5; 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{-2 x} c_2 +{\mathrm e}^{x} c_1 -2 x^{2}-2 x -\frac {11}{2} \]

✓ Mathematica. Time used: 0.015 (sec). Leaf size: 31

ode=D[y[x],{x,2}]+D[y[x],x]-2*y[x]==4*x^2+5; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to -2 x^2-2 x+c_1 e^{-2 x}+c_2 e^x-\frac {11}{2} \]

✓ Sympy. Time used: 0.156 (sec). Leaf size: 26

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-4*x**2 - 2*y(x) + Derivative(y(x), x) + Derivative(y(x), (x, 2)) - 5,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} e^{- 2 x} + C_{2} e^{x} - 2 x^{2} - 2 x - \frac {11}{2} \]