44.5.80 problem 67 (a)

Internal problem ID [7142]
Book : A First Course in Differential Equations with Modeling Applications by Dennis G. Zill. 12 ed. Metric version. 2024. Cengage learning.
Section : Chapter 2. First order differential equations. Section 2.2 Separable equations. Exercises 2.2 at page 53
Problem number : 67 (a)
Date solved : Sunday, March 30, 2025 at 11:48:44 AM
CAS classification : [_separable]

\begin{align*} \left (2 y+2\right ) y^{\prime }-4 x^{3}-6 x&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=-3 \end{align*}

✓ Maple. Time used: 0.078 (sec). Leaf size: 20

ode:=(2*y(x)+2)*diff(y(x),x)-4*x^3-6*x = 0; 
ic:=y(0) = -3; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ y = -1-\sqrt {x^{4}+3 x^{2}+4} \]

✓ Mathematica. Time used: 0.131 (sec). Leaf size: 23

ode=(2*y[x]+2)*D[y[x],x]-(4*x^3+6*x)==0; 
ic={y[0]==-3}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to -\sqrt {x^4+3 x^2+4}-1 \]

✓ Sympy. Time used: 0.517 (sec). Leaf size: 19

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-4*x**3 - 6*x + (2*y(x) + 2)*Derivative(y(x), x),0) 
ics = {y(0): -3} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = - \sqrt {x^{4} + 3 x^{2} + 4} - 1 \]