38.2.37 problem 34 (a)

Internal problem ID [8255]
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 : 34 (a)
Date solved : Tuesday, September 30, 2025 at 05:20:31 PM
CAS classification : [_separable]

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

With initial conditions

\begin{align*} y \left (2\right )&=-4 \\ \end{align*}

✓ Maple. Time used: 0.030 (sec). Leaf size: 15

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

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

✓ Mathematica. Time used: 0.027 (sec). Leaf size: 18

ode=y[x]*D[y[x],x]==3*x; 
ic={y[2]==-4}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -\sqrt {3 x^2+4} \end{align*}

✓ Sympy. Time used: 0.225 (sec). Leaf size: 14

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

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