Find the curve which satisfy the equation xy=(1+x²)dy/dx and passes through point (0, 1)

Question

First other differential equation using Method of separation variable.

Answer 1

The DE can be written:

dy/y=xdx/(1+x²) which can be integrated on both sides:

ln(y)=½ln(1+x²)+C=ln(a)+ln√(1+x²)=ln(a√(1+x²) where a is a constant.

That is: y=a√(1+x²).

Now plug in (0,1):

1=a√1, so a=1 and y=√(1+x²).