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 : Monday, January 27, 2025 at 02:39:02 PM
CAS classification : [_separable]

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

With initial conditions

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

✓ Solution by Maple

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

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

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

✓ Solution by Mathematica

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

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

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