Internal problem ID [19]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 1.3. Slope fields and solution curves. Page 26
Problem number: 11.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime }-2 x^{2} y^{2}=0} \end {gather*} With initial conditions \begin {align*} [y \relax (1) = -1] \end {align*}
✓ Solution by Maple
Time used: 0.02 (sec). Leaf size: 15
dsolve([diff(y(x),x) = 2*x^2*y(x)^2,y(1) = -1],y(x), singsol=all)
\[ y \relax (x ) = -\frac {3}{2 x^{3}+1} \]
✓ Solution by Mathematica
Time used: 0.15 (sec). Leaf size: 16
DSolve[{y'[x] == 2*x^2*y[x]^2,y[1]==-1},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {3}{2 x^3+1} \\ \end{align*}