30.6.2 problem 2

Internal problem ID [7537]
Book : Fundamentals of Differential Equations. By Nagle, Saff and Snider. 9th edition. Boston. Pearson 2018.
Section : Chapter 2, First order differential equations. Review problems. page 79
Problem number : 2
Date solved : Tuesday, September 30, 2025 at 04:44:59 PM
CAS classification : [[_linear, `class A`]]

\begin{align*} y^{\prime }-4 y&=32 x^{2} \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 20

ode:=diff(y(x),x)-4*y(x) = 32*x^2; 
dsolve(ode,y(x), singsol=all);
 

\[ y = -8 x^{2}-4 x -1+{\mathrm e}^{4 x} c_1 \]

✓ Mathematica. Time used: 0.031 (sec). Leaf size: 33

ode=D[y[x],x]-4*y[x]==32*x^2; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to e^{4 x} \left (\int _1^x32 e^{-4 K[1]} K[1]^2dK[1]+c_1\right ) \end{align*}

✓ Sympy. Time used: 0.081 (sec). Leaf size: 19

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-32*x**2 - 4*y(x) + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} e^{4 x} - 8 x^{2} - 4 x - 1 \]