What is the solution for y^'=x^2sec(y) ?

The solution for y^'=x^2sec(y) is y=arcsin((x^3)/3+c_{1})+2pin,y=pi+arcsin(-(x^3)/3-c_{1})+2pin

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y^'=x^2sec(y)

y^{^{'}} = x^{2} sec (y)

y = arcsin (\frac{x ^{3}}{3} + c_{1}) + 2 πn, y = π + arcsin (- \frac{x ^{3}}{3} - c_{1}) + 2 πn

Solution steps

y^{'} (x) = x^{2} sec (y)

Solve separable ODE:

y = arcsin (\frac{x ^{3}}{3} + c_{1}) + 2 πn, y = π + arcsin (- \frac{x ^{3}}{3} - c_{1}) + 2 πn

y = arcsin (\frac{x ^{3}}{3} + c_{1}) + 2 πn, y = π + arcsin (- \frac{x ^{3}}{3} - c_{1}) + 2 πn

\int_{0}^{1} x e^{- 3 x^{2}} d x

n = 0 \sum \infty arctan (2 n)

(2, 2), (0, - 1)

x \to 0 - lim (\frac{5}{sin ( x )})

a cos (2 π + θ)

What is the solution for y^'=x^2sec(y) ?
The solution for y^'=x^2sec(y) is y=arcsin((x^3)/3+c_{1})+2pin,y=pi+arcsin(-(x^3)/3-c_{1})+2pin