38.2.38 problem 34 (b)

Internal problem ID [8256]
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 (b)
Date solved : Tuesday, September 30, 2025 at 05:20:33 PM
CAS classification : [_separable]

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

With initial conditions

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

✓ Maple. Time used: 0.049 (sec). Leaf size: 18

ode:=y(x)*diff(y(x),x) = 3*x; 
ic:=[y(0) = 0]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\begin{align*} y &= \sqrt {3}\, x \\ y &= -\sqrt {3}\, x \\ \end{align*}

✓ Mathematica. Time used: 0.027 (sec). Leaf size: 36

ode=y[x]*D[y[x],x]==3*x; 
ic={y[0]==0}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.229 (sec). Leaf size: 29

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

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