The general solution of the equation

is y(x) = tan(C + sin x) With the initial condition y(0) = 0 the solution y(x) = tan(sin x) is well behaved. But with y(0) = 1 the solution y(x) = tan (1/4π sin x) has a vertical asymptote at x = sin^-1 (π/4) ≈ 0.90334. Use Euler’s method to verify this fact empirically.

Transcribed Image Text:

dy dx = = (1 + y²) cos x ||