8.2.9 problem 11

Internal problem ID [669]
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
Date solved : Wednesday, February 05, 2025 at 03:51:04 AM
CAS classification : [_separable]

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

With initial conditions

\begin{align*} y \left (1\right )&=-1 \end{align*}

✓ Solution by Maple

Time used: 0.013 (sec). Leaf size: 15

dsolve([diff(y(x),x) = 2*x^2*y(x)^2,y(1) = -1],y(x), singsol=all)
 

\[ y = -\frac {3}{2 x^{3}+1} \]

✓ Solution by Mathematica

Time used: 0.122 (sec). Leaf size: 16

DSolve[{D[y[x],x] == 2*x^2*y[x]^2,y[1]==-1},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -\frac {3}{2 x^3+1} \]