It is given that `e^y=(1+x^2)*C-1`
To isolate y, take the natural logarithm of both the sides.
=> `ln(e^y) = ln((1 + x^2)*C - 1)`
Use the property `log a^b = b*log a`
=> `y*ln e = ln((1 + x^2)*C - 1)`
The base of natural logarithm is e and `log_b b = 1`
=> `y = ln((1 + x^2)*C - 1)`
The required expression for y is `y = ln((1 + x^2)*C - 1)`
Do you want to express something like, y = function of x, then the solution is given below:
Given expression is:
e^y = (1+x^2)C - 1
Take natural log(log with base e) on both sides:
log [e^y] = log [ (1+x^2 )*C - 1]
=> y = log [ (1+x^2 )*C - 1]
Which is in the desired form.