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PUNE MCA Exam 2014 Question Paper with answers for online practice

Question : 9 of 58

Marks: +1, -0

The differential equation Xdy - ydx = 0 representes

Solution:

Concept:

The equation can be separated and integrated to find the relationship between x and y.

Explanation:

Given:

x\,dy - y\,dx = 0

Separate variables:

x\,dy = y\,dx

Assuming

x \neq 0

y \neq 0

\frac{dy}{y} = \frac{dx}{x}

Integrate both sides:

\ln |y| = \ln |x| + C

Exponentiate:

|y| = e^C |x|

Let

e^C = k

(positive constant):

y = \pm k x

, i.e.,

y = mx

, where

m

is a constant.

This is the equation of a straight line through the origin.

Answer:

straight line

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