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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

 
Answers (1)
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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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