ytan(x)(dy)/(dx)=(4+y^2)sec(x^2)

解答

y tan (x) \frac{d y}{d x} = (4 + y^{2}) sec (x^{2})

y = e^{2 \cdot \int s e c (x^{2}) c o t (x) d x} - 4, y = - e^{2 \cdot \int s e c (x^{2}) c o t (x) d x} - 4

求解步骤

y tan (x) \frac{d y}{d x} = (4 + y^{2}) sec (x^{2})

求解可分离方程:

y = e^{2 \cdot \int s e c (x^{2}) c o t (x) d x} - 4, y = - e^{2 \cdot \int s e c (x^{2}) c o t (x) d x} - 4

y = e^{2 \cdot \int s e c (x^{2}) c o t (x) d x} - 4, y = - e^{2 \cdot \int s e c (x^{2}) c o t (x) d x} - 4

\frac{d y}{d x} = c \cdot y

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

y^{^{'}} = 7 x y

\frac{1}{y} d y = d x

(x + x y) y^{^{'}} + y = 0