85.49.3 problem 1 (c)

Internal problem ID [22804]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter 4. Linear differential equations. A Exercises at page 194
Problem number : 1 (c)
Date solved : Thursday, October 02, 2025 at 09:14:46 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-4 y&=8 x^{2} \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 23

ode:=diff(diff(y(x),x),x)-4*y(x) = 8*x^2; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.01 (sec). Leaf size: 28

ode=D[y[x],{x,2}]-4*y[x]==8*x^2; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.062 (sec). Leaf size: 22

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-8*x**2 - 4*y(x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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