The differential equation from y=Ke^{\sin ^{-1}x}+3 is

  • Option 1)

    \sqrt{1-x^{2}} \: \frac{dy}{dx}=y+3

  • Option 2)

    \sqrt{1-x^{2}} \: \: \frac{dy}{dx}=y-3

  • Option 3)

    \sqrt{1+x^{2}} \: \: \frac{dy}{dx}=y+3

  • Option 4)

    None of these

 

Answers (1)

 

Differential Equations -

An equation involving independent variable (x), dependent variable (y) and derivative of dependent variable with respect to independent variable 
\left (\frac{\mathrm{d} y}{\mathrm{d} x} \right )

- wherein

eg:

  \frac{d^{2}y}{dx^{2}}- 3\frac{dy}{dx}+5x=0

 

 y=Ke^{\sin ^{-1}x}+3

\frac{dy}{dx}=K.e^{\sin -1x} \times \frac{1}{\sqrt{1-x^{2}}}=\frac{y-3}{\sqrt{1-x^{2}}}

\therefore \sqrt{1-x^{2}} \frac{dy}{dx}= (y-3)

 


Option 1)

\sqrt{1-x^{2}} \: \frac{dy}{dx}=y+3

Incorrect

Option 2)

\sqrt{1-x^{2}} \: \: \frac{dy}{dx}=y-3

correct

Option 3)

\sqrt{1+x^{2}} \: \: \frac{dy}{dx}=y+3

Incorrect

Option 4)

None of these

Incorrect

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