y1 dydx 1x21 fpr y0 Sol x21 dy dx Integrate yx21 x c y

y1 = dy/dx = 1/x2-1 fpr y(0) Sol (x2-1) dy = dx Integrate = y(x2-1) = x + c (y(0) = 0 = c = 0) y = x/x2-1 y1 = x2-1-x(2x)/(x2-1)2 = -x2-1/(x2-1)2 1/x2-1 why which stop I went wrong

Solution

in the first step,integrating LHS (x^2-1)dy is not (x^2-1) dy

since y is not independent of x

Actual solution :

dy = dx/(x^2-1)

=>

y = [ln(x-1) -ln(x+1)]/2