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Solve the differential equation dy/dx - ytanx = -y^2secx

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Solve the differential equation dy/dx - ytanx = -y2secx

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Best answer

Rewriting the given equation

y-2(dy/dx) - y-1tanx = - secx

Let y-1 = v. Then

-y2(dy/dx) = dv/dx

Therefore,

Multiplying Eq. (1) by secx and integrating

vsecx = ∫sec2xdx = tanx + c

Thus, the required solution is secx/y = tanx + c.

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