What is the solution for y^'+x^2sec(y)=0 ?

The solution for y^'+x^2sec(y)=0 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)=0

y^{^{'}} + x^{2} sec (y) = 0

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) = 0

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

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What is the solution for y^'+x^2sec(y)=0 ?
The solution for y^'+x^2sec(y)=0 is y=arcsin(-(x^3)/3+c_{1})+2pin,y=pi+arcsin((x^3)/3-c_{1})+2pin