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  • The differential equation of the curve for which the initial ordinate of any tangent is equal to the corresponding subnormal  Option: 1</st

The differential equation of the curve for which the initial ordinate of any tangent is equal to the corresponding subnormal
 

Option: 1

 is linear


Option: 2

 is homogeneous of first degree


Option: 3

 has separable variables


Option: 4

 is second order


Answers (1)

best_answer

If y=f(x) is the curve, Y-y=f^{\prime}(x)(X-x) is the equation of the tangent at (x, y), with f^{\prime}(x)=\frac{d y}{d x} putting X=0, the initial ordinate of the tangent is therefore y-x f^{\prime}(x). The subnormal at this point is given by y \frac{d y}{d x}
So, \quad y \frac{d y}{d x}=y-x \frac{d y}{d x} \Rightarrow \frac{d y}{d x}=\frac{y}{x+y}
Homogeneous equation,

\frac{d x}{d y}=\frac{x+y}{y}=\frac{x}{y}+1 \text { or } \frac{d x}{d y}-\frac{x}{y}=1
It is a linear equation.

Posted by

Ajit Kumar Dubey

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