The differential equation which represents the family of curves y= c_{1}e^{c_{2}x}, where c_{1}\: and\: c_{2} are arbitrary constants, is

  • Option 1)

    y{}''= {y}'y

  • Option 2)

    y{y}''= {y}'

  • Option 3)

    y{y}''= \left ( {y}' \right )^{2}

  • Option 4)

    {y}'= y^{2}

 

Answers (1)

As we learnt in 

Formation of Differential Equations -

A differential equation can be derived from its equation by the process of differentiation and other algebraical process of elimination

-

 

y=C_{1}.e^{C_{2}x}

y'=C_{1}.e^{C_{2}x}\times C_{2} \Rightarrow C_{1}C_{2}.e^{C_{2}x}=C_{2}y

y"=C_{2}.y'

\Rightarrow \frac{y'}{y''}=\frac{y}{y'}

\Rightarrow yy''=(y')^{2}

 


Option 1)

y{}''= {y}'y

This is incorrect option

Option 2)

y{y}''= {y}'

This is incorrect option

Option 3)

y{y}''= \left ( {y}' \right )^{2}

This is correct option

Option 4)

{y}'= y^{2}

This is incorrect option

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