8.6.30 problem 31(a)

Internal problem ID [800]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Chapter 1 review problems. Page 78
Problem number : 31(a)
Date solved : Tuesday, March 04, 2025 at 11:49:48 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=3 x^{2} \left (7+y\right ) \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 12

ode:=diff(y(x),x) = 3*x^2*(7+y(x)); 
dsolve(ode,y(x), singsol=all);
 

\[ y = -7+{\mathrm e}^{x^{3}} c_1 \]

✓ Mathematica. Time used: 0.026 (sec). Leaf size: 20

ode=D[y[x],x] == 3*x^2*(7+y[x]); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to -7+c_1 e^{x^3} \\ y(x)\to -7 \\ \end{align*}

✓ Sympy. Time used: 0.258 (sec). Leaf size: 10

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-3*x**2*(y(x) + 7) + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} e^{x^{3}} - 7 \]