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Form the differential equations correspo...

Form the differential equations corresponding to the family of curves.
(i) y = c(x-2c) where c is a parameter.
(ii) y = a cos 3x + b sin 3x where a, b are parameters.
(iii) y = a cos x + b sin x where a, b are parameters.
(iv) `y = a e^(x) + b e^(-x)` where a, b are parameters.

Text Solution

Verified by Experts

The correct Answer is:
(i) `y = xy_(1) - 2y_(1)^(2)` (ii) `y_(2) + 9y = 0`
(iii) `y_(2) + y = 0` (iv) `y_(2) = y`
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