Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Engineering
  • 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

View full answer

JEE Main high-scoring chapters and topics

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

Similar Questions

Trending Articles/News

anam-khan

Is it difficult to get into NIT Durgapur? JEE Main cut-offs for BTech programmes
anam-khan

JEE Main Deleted Syllabus 2025: Topics to skip this year; why no optional questions?
anam-khan

NTA Exam 2025 Live: UGC NET admit card out for all exams; JEE Main session 1 hall ticket soon

Latest Question