7.7.31 problem 31

Internal problem ID [209]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 1. First order differential equations. Review problems at page 98
Problem number : 31
Date solved : Saturday, March 29, 2025 at 04:46:08 PM
CAS classification : [_separable]

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

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

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

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

✓ Mathematica. Time used: 0.062 (sec). Leaf size: 20

ode=D[y[x],x]==3*(y[x]+7)*x^2; 
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: 0.270 (sec). Leaf size: 10

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x**2*(3*y(x) + 21) + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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