What is the solution for y^'=8xsec(y) ?

The solution for y^'=8xsec(y) is y=arcsin(4x^2+c_{1})+2pin,y=pi+arcsin(-4x^2-c_{1})+2pin

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y^'=8xsec(y)

y^{^{'}} = 8 x sec (y)

y = arcsin (4 x^{2} + c_{1}) + 2 πn, y = π + arcsin (- 4 x^{2} - c_{1}) + 2 πn

Solution steps

y^{'} (x) = 8 x sec (y)

Solve separable ODE:

y = arcsin (4 x^{2} + c_{1}) + 2 πn, y = π + arcsin (- 4 x^{2} - c_{1}) + 2 πn

y = arcsin (4 x^{2} + c_{1}) + 2 πn, y = π + arcsin (- 4 x^{2} - c_{1}) + 2 πn

e^{x} tan (y) d x + (1 - e^{x}) sec^{2} (y) d y = 0

x cos (y) + 1 - x^{2} sin (y) y^{^{'}} = 0

(5 x + 4) + (5 y - 5) y^{^{'}} = 0

y^{^{'}} (x) = (1 - y^{2}) tan (x), y (0) = 3

\frac{d y}{d x} = \frac{- 0.9}{cos ( y )}, y (0) = \frac{π}{3}

What is the solution for y^'=8xsec(y) ?
The solution for y^'=8xsec(y) is y=arcsin(4x^2+c_{1})+2pin,y=pi+arcsin(-4x^2-c_{1})+2pin