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# X^-1dy/dx = 2cos^2y, y(0) = 𝜋/4?

can i get the answer ASAP please?

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- 2 months agoFavorite Answer
dy / (x * dx) = 2 * cos(y)^2

dy / cos(y)^2 = 2x * dx

sec(y)^2 * dy = 2x * dx

Integrate

tan(y) = x^2 + C

y = pi/4 when x = 0

tan(pi/4) = 0^2 + C

1 = 0 + C

1 = C

tan(y) = x^2 + 1

y = arctan(x^2 + 1)

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Thank you so much sir :)