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Question

Solve the differential equation :
dydx=−2x+y+14x+2y−1

A
log(2x+y1)+x+2y=c
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B
log(2xy)+2x+y+1=c
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C
log(2xy+1)+x2y=c
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D
log(2xy1)+x+2y=c
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Solution

The correct option is A log(2x+y1)+x+2y=c
dydx=2x+y+14x+2y1
Substitute 2x+y=t2+dydx=dtdx
dtdx2=t+12t1dtdx=3(t1)2t1dtdx2t13(t1)=1dt2t13(t1)=dxlog(2x+y1)+x+2y=c

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