44.2.49 problem 52

Internal problem ID [6981]
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 : 52
Date solved : Monday, January 27, 2025 at 02:39:40 PM
CAS classification : [_separable]

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

With initial conditions

\begin{align*} y \left (2\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.038 (sec). Leaf size: 9

dsolve([diff(y(x),x)=x*sqrt(y(x)),y(2) = 1],y(x), singsol=all)
 

\[ y = \frac {x^{4}}{16} \]

✓ Solution by Mathematica

Time used: 0.136 (sec). Leaf size: 27

DSolve[{D[y[x],x]==x*Sqrt[y[x]],{y[2]==1}},y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {x^4}{16} \\ y(x)\to \frac {1}{16} \left (x^2-8\right )^2 \\ \end{align*}