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Question

The solution of the differential equation (x2+y2)dx-2xydy=0 is


A

x2-y2=Cx

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B

x2-y2=Cy

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C

x2+y2=Cx

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D

x2+y2=Cy

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Solution

The correct option is A

x2-y2=Cx


Explanation of the correct option.

Compute the required value.

Given : (x2+y2)dx-2xydy=0

x2+y2dx=2xydy

dydx=x2+y22xy…………..1

Let y=vx

Differentiate with respect to x,

dydx=v+xdvdx

Substitute the value in the equation 1.

v+xdvdx=x2+(vx)22x(vx)

v+xdvdx=1+v22v

xdvdx=1+v22v-v

xdvdx=1+v2-2v22v

dxx=2v1-v2dv

Integrate both sides,

logx=-log1-v2+logC

logx1-v2=logC

x1-y2x2=C

xx2-y2x2=C

x2-y2=Cx

Hence option A is the correct option.


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