InterviewSolution
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InterviewSolution
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The solution of dy = cos x `(2 - y " cosec " x) dx` , where ` y = sqrt(2) , " when " x = pi//4 ` isA. ` y = sin x +1/2 "cosec"x`B. ` y = tan (x//2)+cot(x//2)`C. `y = (1//sqrt(2))sec (x//2)+sqrt(2)cos (x//2)`D. None of the above |
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Answer» Correct Answer - b Given , `(dy)/(dx) = 2 cos x - y cos x "cosec " x` ` rArr (dy)/(dx) + y cot x = 2 cos x ` which is linear differential equation . ` :. IF = e^(int cot x dx ) = e ^(log (sin x) ) = sin x ` ` :. " Required Solution is " y * sin x = int 2 cos x sin x dx +c` ` rArr y sin x = int sin 2 x dx +C` , ` rArr y sin x = (- cos 2 x)/2 +C ` Given at ` x = pi/4 , y = sqrt(2)` ` :. sqrt(2) sin . pi/4 = (- cos 2(pi //4))/2 +C` ` rArr C = 1` ` :. y sin x = -1/2 cos 2 x +1` ` rArr y = -1/2 * (cos 2x)/(sinx) + " cosec " x ` ` rArr y = 1/(2sin x ) (1-2 sin^(2)x) + " cosec " x` ` rArr y = 1/2 " cosec " x + sin x ` |
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