(dy)/(dx)=(1+y^2)tan(x),y(0)=sqrt(3)

Lösung

\frac{d y}{d x} = (1 + y^{2}) tan (x), y (0) = 3

y = tan (- ln (cos (x)) + \frac{π}{3})

Schritte zur Lösung

\frac{d y}{d x} = (1 + y^{2}) tan (x)

Solve separable ODE:

y = tan (- ln (cos (x)) + \frac{π}{3})

y = tan (- ln (cos (x)) + \frac{π}{3})

3 (1 + t^{2}) d y = 2 t y (y^{3} - 1) d t

y^{^{'}} = y^{2} - 9

(x y + 2 y) d x + x d y = 0

8 y^{2} (x d y + y d x) = y d x - x d y

y^{^{'}} = x y - x y^{2}