38.2.36 problem 33 (c)

Internal problem ID [8254]
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 : Tuesday, September 30, 2025 at 05:20:28 PM
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: 0.030 (sec). Leaf size: 13

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

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

✓ Mathematica. Time used: 0.056 (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]
 

\begin{align*} y(x)&\to \sqrt {3} \sqrt {x^2-1} \end{align*}

✓ Sympy. Time used: 0.224 (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)
 

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