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Question
Verify that the given function (explicit or implicit) is a solution of the corresponding differential equation:
y – cos y = x : (y sin y + cos y + x) y′ = y
Solution
y - cos y = 3x
y’ + sin y : y’ = 1
y (1 + sin y) = 1
⇒ y’ = `1/(1 + sin y)`
Putting the values of y' and y in the differential equation (y sin y + cos y + x) y’ = y
L.H.S. {(x + cos y) sin y + cosy + x}· `1/(1 + sin y)`
⇒ x + cos y = y
R.H.S. Hence, the given function y - cos y = 3x is a solution of the given differential equation.
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