Question

Calculus Help:
Show that ln(y)=arctan(x) is a solution to the differential equation (1+x^2)y"+(2x-1)y'=0
I'm totally lost need help!

Answer 1

From ln(y)=arcxtan(x), raise to power of e
e^(ln(y))=e^(arctan(x))
y=e^arctan(x)
now differentiate y to get y', and differentiate twice to get y".
Substitute in the given equation's LHS to show that after simplification, the LHS = 0 (for any value of x).

Answer 2

Hint: you will need the chain rule to do the differentiations.

Answer 3

Thank you so much mathmate!
you're a lifesaver :)

Answer 4

You're welcome! :)