Internal problem ID [4248]
Book: Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley.
2006
Section: Chapter 8, Ordinary differential equations. Section 2. Separable equations. page
398
Problem number: 8.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime }+2 x y^{2}=0} \end {gather*} With initial conditions \begin {align*} [y \relax (2) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.094 (sec). Leaf size: 11
dsolve([diff(y(x),x)+2*x*y(x)^2=0,y(2) = 1],y(x), singsol=all)
\[ y \relax (x ) = \frac {1}{x^{2}-3} \]
✓ Solution by Mathematica
Time used: 0.194 (sec). Leaf size: 12
DSolve[{y'[x]+2*x*y[x]^2==0,{y[2]==1}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{x^2-3} \\ \end{align*}