Solve the differential equation : dydx=â2x+y+14x+2yâ1
A
log(2x+y−1)+x+2y=c
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B
log(2x−y)+2x+y+1=c
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C
log(2x−y+1)+x−2y=c
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D
log(2x−y−1)+x+2y=c
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Solution
The correct option is Alog(2x+y−1)+x+2y=c dydx=−2x+y+14x+2y−1 Substitute 2x+y=t⇒2+dydx=dtdx dtdx−2=−t+12t−1⇒dtdx=3(t−1)2t−1⇒dtdx2t−13(t−1)=1⇒∫dt2t−13(t−1)=∫dx⇒log(2x+y−1)+x+2y=c