Math, asked by ankit1432003, 9 months ago

Differential equation of xdy÷dx-y=0

Answers

Answered by rishu6845

Answer:

y = kx

Step-by-step explanation:

Given--->

----------

x dy / dx - y = 0

To find---> Solution of given differential

----------- equation

Solution--->

--------------

x dy / dx - y = 0

It is a differential equation of first order and first degree

We solve it by seperation of variables

in simple words collecting terms of x at one side and collecting terms of y at other side

Now

x dy / dx = y

x dy = y dx

dy / y = dx / x

Now variables are seperated

Integrating both sides

∫dy / y = ∫ dx / x +c

We have a intregation formula

∫ 1/ x d x =logx

applying it here

=> log y = log x + c

=> log y = logx + logk ,where c= log k

=> log y = log kx

=> y = kx

So y = kx is general solution of differential equation

Answered by Aɾꜱɦ

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y=yx

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