What is the solution for e^xtan(y)dx+(1-e^x)sec^2(y)dy=0 ?

The solution for e^xtan(y)dx+(1-e^x)sec^2(y)dy=0 is y=arctan(e^{c_{1}}-e^{c_{1}+x})+pin

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e^xtan(y)dx+(1-e^x)sec^2(y)dy=0

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

y = arctan (e^{c_{1}} - e^{c_{1} + x}) + πn

Solution steps

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

Solve separable ODE:

y = arctan (e^{c_{1}} - e^{c_{1} + x}) + πn

y = arctan (e^{c_{1}} - e^{c_{1} + x}) + πn

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}

e^{2 x} d y + 2 y d x = 0

What is the solution for e^xtan(y)dx+(1-e^x)sec^2(y)dy=0 ?
The solution for e^xtan(y)dx+(1-e^x)sec^2(y)dy=0 is y=arctan(e^{c_{1}}-e^{c_{1}+x})+pin