- (E) The solution curve is y = tan x, which we can obtain from the differential equation y ′ = 1 + y^2
with the condition y(0) = 0 as follows:
Since y(0) = 0, C = 0. Verify that (A) through (D) are incorrect.
NOTE: In matching slope fields and differential equations in Questions 25–29, keep in mind that if
the slope segments along a vertical line are all parallel, signifying equal slopes for a fixed x, then
the differential equation can be written as y ′ = f (x). Replace “vertical” by “horizontal” and “x” by
“ y” in the preceding sentence to obtain a differential equation of the form y ′ = g(y).
