44.2.38 problem 34 (b)

Internal problem ID [6970]
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 : Monday, January 27, 2025 at 02:39:12 PM
CAS classification : [_separable]

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

With initial conditions

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

✓ Solution by Maple

Time used: 0.008 (sec). Leaf size: 18

dsolve([y(x)*diff(y(x),x)=3*x,y(0) = 0],y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.043 (sec). Leaf size: 36

DSolve[{y[x]*D[y[x],x]==3*x,{y[0]==0}},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*}