36.1.22 problem 22

Internal problem ID [6277]
Book : Fundamentals of Differential Equations. By Nagle, Saff and Snider. 9th edition. Boston. Pearson 2018.
Section : Chapter 2, First order differential equations. Section 2.2, Separable Equations. Exercises. page 46
Problem number : 22
Date solved : Monday, January 27, 2025 at 01:52:55 PM
CAS classification : [_separable]

\begin{align*} x^{2}+2 y^{\prime } y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=2 \end{align*}

✓ Solution by Maple

Time used: 0.036 (sec). Leaf size: 15

dsolve([x^2+2*y(x)*diff(y(x),x)=0,y(0) = 2],y(x), singsol=all)
 

\[ y = \frac {\sqrt {-3 x^{3}+36}}{3} \]

✓ Solution by Mathematica

Time used: 0.103 (sec). Leaf size: 18

DSolve[{x^2+2*y[x]*D[y[x],x]==0,{y[0]==2}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \sqrt {4-\frac {x^3}{3}} \]