If y=y(x) satisfies the differential equation 8x(9+x)dy=(4+9+x)−1dx,  x>0 and y(0)=7 then y(256)=

dy=dx8x9+x4+9+x Let 4+9+x=t⇒129+x⋅12xdx=dt∴dy=dt2tIntegrating on both sidesy=t+c=4+9+x+c put x=0, y(0)=77=4+9+0+c c=0y(256)=4+9+256=4+9+16=4+5=3