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  • Tell me? Which of the following is a linear diffrential equation ?

Which of the following is a linear diffrential equation ? 

  • Option 1)

    \sin x \frac{dy}{dx} = \cos x (1-y)

  • Option 2)

    \sin x \frac{dy}{dx} = \cos y(1-x)

  • Option 3)

    \sin y \frac{dy}{dx} = \cos x (1-y)

  • Option 4)

    None  of these 

 

Answers (1)

best_answer

As we have learned

Linear Differential Equation -

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

- wherein

P, Q are functions of x alone.

 

(A)\rightarrow \sin x \frac{dy}{dx} = \cos x (1-y)\Rightarrow dy/dx = \cot (1-y)

\Rightarrow dy/dx + (\cot x)y = \cot x

 where P and Q bothe are one function of x alone 

(B)\rightarrow \sin x \frac{dy}{dx} = \cos y(1-x)

\Rightarrow dy/dx = \cos y/ \sin x - \left ( \frac{\cos y}{ \sin x} \right )x = \frac{\cos y}{\sin x}

It is not a form of linear diffrential equation 

(C)\rightarrow \sin y \frac{dy}{dx} = \cos x (1-y)

\Rightarrow dy/dx = \cos x/ \sin y - \left ( \frac{\cos y}{ \sin x} \right )y = \frac{\cos x}{\sin y}

here P and Q are not function of x alone 


Option 1)

\sin x \frac{dy}{dx} = \cos x (1-y)

Option 2)

\sin x \frac{dy}{dx} = \cos y(1-x)

Option 3)

\sin y \frac{dy}{dx} = \cos x (1-y)

Option 4)

None  of these 

Posted by

gaurav

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