44.2.36 problem 33 (c)

Internal problem ID [6968]
Book : A First Course in Differential Equations with Modeling Applications by Dennis G. Zill. 12 ed. Metric version. 2024. Cengage learning.
Section : Chapter 1. Introduction to differential equations. Section 1.2 Initial value problems. Exercises 1.2 at page 19
Problem number : 33 (c)
Date solved : Wednesday, March 05, 2025 at 04:00:20 AM
CAS classification : [_separable]

\begin{align*} y y^{\prime }&=3 x \end{align*}

With initial conditions

\begin{align*} y \left (-2\right )&=3 \end{align*}

✓ Maple. Time used: 0.033 (sec). Leaf size: 13

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

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

✓ Mathematica. Time used: 0.084 (sec). Leaf size: 20

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

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

✓ Sympy. Time used: 0.449 (sec). Leaf size: 12

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

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