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# I have a doubt, kindly clarify. Which of the following is a linear diffrential equation ?

Which of the following is a linear diffrential equation ?

• Option 1)

$dy/dx + (\sin x )y = \cos y$

• Option 2)

$dy/dx + (\sin y)y = \cos x$

• Option 3)

$dy/dx + (\sin y)y = \cos y$

• Option 4)

$dy/dx + (\sin x )y = \cos x$

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As we have learned

Equations Reducible to the homogeneous form -

$\frac{dy}{dx}=\frac{dY}{dx}\times\frac{dx}{dX} =\frac{dY}{dX}$

- wherein

$x= X+h$

$y= Y+k$

Equations Reducible to the homogeneous form -

$\frac{dy}{dx}=\frac{ax+by+c}{Ax+By+C}$

- wherein

$x=X+h$

$y=Y+k$

Linear Differential Equation -

$\frac{dy}{dx}+Py= Q$

- wherein

P, Q are functions of x alone.

$dy/dx + py = Q$   is a linear diffrential equation , when P and Q are function of x alone

only option (B) has P and Q are function of x only

Option 1)

$dy/dx + (\sin x )y = \cos y$

Option 2)

$dy/dx + (\sin y)y = \cos x$

Option 3)

$dy/dx + (\sin y)y = \cos y$

Option 4)

$dy/dx + (\sin x )y = \cos x$

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