Trigonometric EquationHard

Question

= (x3 - 2xsin-1y)
General solution will be

Options

A.2sin-1y = (x2 - 1) + C e-x2
B.2cos-1y = (x4 + 1) + C
C.ex2 sin-1y = (x2 - x) + C
D.2cos-1y = (x2 - 1) e-x2 + C

Solution

= x3 - 2x sin-1y
+ 2x sin-1y = x3
let sin-1 y = t

+ 2xt = x3
I.F. = e∫2xdx = ex2
∴ solution is given by
t(ex2) = ∫x3 .ex2 dx + c let x2 = t
sin-1y ex2 = + c 2ndx = dt
⇒ 2sin-1 y ex2 = (t.et - ∫etdt) + 2C
⇒ 2sin-1 y ex2 = (x2 - 1) ex2 + K
⇒ 2sin-1 y = (x2 -1) + k ex2

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