Question

Find the solution of y′=2xy2

Answer 1

Answer on Question #69639 – Math – Differential Equations

Question

Find the solution of

$$y' = 2xy^2$$

Solution

$$y' = 2xy^2,$$ $$dy/dx = 2xy^2,$$ $$1/y^2 \cdot dy = 2x \cdot dx,$$ $$\int 1/y^2 \cdot dy = \int 2x \cdot dx,$$ $$-1/y + C = x^2,$$

where $C$ is constant of integration,

$$y = 1/(C - x^2).$$

Answer: $y = 1/(C - x^2)$.

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