Internal problem ID [4425]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {x^{2}+2 y y^{\prime }=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 2] \end {align*}
✓ Solution by Maple
Time used: 0.029 (sec). Leaf size: 15
dsolve([x^2+2*y(x)*diff(y(x),x)=0,y(0) = 2],y(x), singsol=all)
\[ y \relax (x ) = \frac {\sqrt {-3 x^{3}+36}}{3} \]
✓ Solution by Mathematica
Time used: 0.075 (sec). Leaf size: 18
DSolve[{x^2+2*y[x]*y'[x]==0,{y[0]==2}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \sqrt {4-\frac {x^3}{3}} \\ \end{align*}