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

Create a free account to view solution

View Solution Free
Topic: Trigonometric Equation·Practice all Trigonometric Equation questions

More Trigonometric Equation Questions

Total number of integral values of ′n′ so that sin x (sin x + cos x) = n has at least one solution is-...A particle has two velocities of equal magnitude inclined to each other at an angle θ. If one of them is halved, th...If f(x) = cos-1 + xx then at x = 1, f ′(x) is equal to...The solution set of the equation 4sinθ cosθ − 2 cosθ − 2√3 sin θ + √3 = 0 in...If ∫(1 + x tan x)-2 dx = + C ; then value of f(x) is...