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  • Confused! kindly explain, If y=mx+c where m and c are arbitrary constants then differential equation corresponding to given family of lines will be

If y=mx+c where m and c are arbitrary constants then differential equation corresponding to given family of lines will be

  • Option 1)

    \left ( \frac{d^{2}y}{dx^{2}} \right )=0

  • Option 2)

    \left ( \frac{dy}{dx} \right )=m

  • Option 3)

    \left ( \frac{dy}{dx} \right )+\left ( \frac{d^{2}y}{dx^{2}} \right )=0

  • Option 4)

    \left ( \frac{d^{2}y}{dx^{2}} \right )=\left ( \frac{dy}{dx} \right )

 

Answers (2)

best_answer

As we learnt

 

Formation of Differential Equations -

 

Let y and x be the dependent and the independent variables respectively. The equation of (x, y, c) = 0 , is family of curves

- wherein

C is the arbitrary Constant

 

 There are two arbitrary constants and hence both must be eliminated.

Differentiating first time we get   \frac{dy}{dx}= m

Again differentiating we get \frac{d^{2}y}{dx^{2}}= 0


Option 1)

\left ( \frac{d^{2}y}{dx^{2}} \right )=0

Option 2)

\left ( \frac{dy}{dx} \right )=m

Option 3)

\left ( \frac{dy}{dx} \right )+\left ( \frac{d^{2}y}{dx^{2}} \right )=0

Option 4)

\left ( \frac{d^{2}y}{dx^{2}} \right )=\left ( \frac{dy}{dx} \right )

Posted by

Himanshu

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JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE

Option 1 is correct 

Posted by

Tadigadapa sandeep

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