Question

Solve the differential equation
\frac{dy}{dx} = 8 x^2 y^2
with the condition that y( 2) = 4.

Answer 1

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Answer 2

\[ \frac{dy}{dx} = 8x^2y^2 \implies \frac{dy}{dx}\frac{1}{y^2} = x^2\]Integrating both sides with respect to x, we are left with: \[ \int \frac{dy}{dx} \frac{1}{y^2} dx= \int x^2 dx \implies \int \frac{dy}{y^2} = \int x^2dx\]Rewrite y^2 as y^(-2). Can you conclude?

Answer 3

tnx