If 2x=y1/5+y−1/5 then (x2−1)d2ydx2+xdydx=
5y
25y
25 y2
y + 25
Consider (y1/5+y−1/5)2=(y1/5−y−1/5)2+4 ∴y1/5−y−1/5=2√x2−1 ∴y1/5=x+√x2−1 ⇒y=(x+√x2−1)5 dydx=5(x+√x2−1)4(1+2x2√x2−1) (x2−1)(dydx)2=25 y2 Again differentiate wrt.x