Questions
The solution of the differential equation is
a
e2(y−2)x+2==c2(x+2)3(x+2y-2).
b
e2(y−2)x+2=c2(x+2)4(x+2y-2)..
c
e2(y−2)x+2=c2(x+2)3(x+2y+2)…
d
e2(y−2)x+2=c2(x+2)3(x-2y+2)
detailed solution
Correct option is A
dydx=(x+y)2(x+2)(y−2)=[(x+2)+(y−2)]2(x+2)(y−2) put X=x+2 and Y=y+2dYdX=(X+Y)2XYput Y=vXv+XdvdX=v2+2v+1v=v+2v+1v⇒Xdvdx=2v+1v⇒v2v+1dv=dxX⇒∫1−11+2vdv=2∫dxXv−12ln|1+2v|=2lnX+lnc2v-ln1+2v=4ln X+2lnc2v=lnc2X4(1+2v)2YX=lnc2X41+2YXe2YX=c2X3(X+2Y)⇒e2(y−2)x+2=c2(x+2)3(x+2+2y−4)=c2(x+2)3(x+2y-2)Talk to our academic expert!
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The general solution of the differential equation is
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