Internal problem ID [4439]
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: 31 part(b.2).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime }-x y^{3}=0} \end {gather*} With initial conditions \begin {align*} \left [y \relax (0) = {\frac {1}{2}}\right ] \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 13
dsolve([diff(y(x),x)=x*y(x)^3,y(0) = 1/2],y(x), singsol=all)
\[ y \relax (x ) = \frac {1}{\sqrt {-x^{2}+4}} \]
✓ Solution by Mathematica
Time used: 0.145 (sec). Leaf size: 16
DSolve[{y'[x]==x*y[x]^3,{y[0]==1/2}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{\sqrt {4-x^2}} \\ \end{align*}