Consider this differential equation for y=y(x) dx/dy = (1+y²) /(1+x²)
Find the general solution, and use it to complete parts (a)-(c) below.
a) Find the solution y(x) for (∗) that satisfies the additional requirement y(0)=0. Determine the largest open interval containing x=0 on which the identity (∗) is valid. (Use interval notation to enter your answer; type "inf" to represent [infinity].)
b) Repeat part (a), but use the modified initial condition y(0)=−2.
c) Repeat part (a), but use the modified initial condition y(0)=7. y(x)=∣, for x∈ Hint: tan(θ+ϕ)= tan(θ)+tan(ϕ)/1−tan(θ)tan(ϕ)