Let y = y(x) be the solution of the differential equation cosx(dy/dx) + 2ysinx = sin2x, x ∈ (0, π/2). If y(π/3) = 0, then y(π/4) is equal to:
Let y = y(x) be the solution of the differential equation cosx(dy/dx) + 2ysinx = sin2x, x ∈ (0, π/2). If y(π/3) = 0, then y(π/4) is equal to:
Option 1 -
2+√2
Option 2 -
(√2-1)/√2
Option 3 -
2-√2
Option 4 -
√2-2
Asked by Shiksha User
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1 Answer
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Correct Option - 4
Detailed Solution:dy/dx + 2tanx · y = 2sinx
I.F. = e^ (∫2tanxdx) = sec²x
Solution is y·sec²x = ∫2sinx·sec²xdx + C
ysec²x = 2secx + C
0 = 2·2 + c ⇒ c = -4
ysec²x = 2secx - 4
y (π/4) = √2 - 2
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