If dy dx equals sine squared of the quantity pi times y over 4 and y = 1 when x = 0, then find the value of x when y = 3

Question

If  and y = 1 when x = 0, then find the value of x when y = 3

A	0
B
C
D	None of these

Answer 1

Ceparate variables: dy/sin²(πy/4) = dx; ∫dy/sin²(πy/4) = ∫dx; - 4/πcot(πy/4) = x + C;

To get C we use intial condition: (0,1); - 4/πcot(π/4) = 0 + C, C = - 4/π and - 4/πcot(πy/4) = x - 4/π.

Let y = 3, - 4/πcot(3π/4) = x - π/4; x = 4/π + π/4;

So if y = 3 then x = (16 + π²)/(4π).