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Question

The solution of (6x+7y4)dx+(7x4y+3)dy=0 is:

A
3x2+7xy2y24x+3y=c
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B
6x24y2+7xy4x+3y=c
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C
3x2+14xy4y24x+3y=c
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D
6x2+4x4y2+4x+3y=c
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Solution

The correct option is A 3x2+7xy2y24x+3y=c
dydx+(6x+7y4)(7x4y+3)=0
put x=X+h;y=Y+k
6h+7k4=0...........1
7h4k+3=0............2
Put Y=vX
v+XdvdX+6+7v74v=0
XdvdX+6+14v4v274v=0
74v3+7v2v2dv+2dXX=logc
logX2(3+7v2v2)=logc
3X2+7XY2Y2=c
3(xh)2+7(xh)(yk)2(yk)2=c
3x2+7xy2y2+x(6h7k)y(4k7h)=c
3x2+7xy2y24x+3y=c [from 1 and 2]



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