(x^2+9)dy=(2x-8xy)dx

解答

(x^{2} + 9) d y = (2 x - 8 x y) d x

y = \frac{c _{1}}{4 ( x ^{8} + 36 x ^{6} + 486 x ^{4} + 2916 x ^{2} + 6561 )} + \frac{1}{4}

求解步骤

(x^{2} + 9) d y = (2 x - 8 x y) d x

求解可分离方程:

y = \frac{c _{1}}{4 ( x ^{8} + 36 x ^{6} + 486 x ^{4} + 2916 x ^{2} + 6561 )} + \frac{1}{4}

y = \frac{c _{1}}{4 ( x ^{8} + 36 x ^{6} + 486 x ^{4} + 2916 x ^{2} + 6561 )} + \frac{1}{4}

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

\frac{d y}{d x} = - 2 y + 5

x^{3} \frac{d y}{d x} = y^{2} (x - 3)

(t^{3} + 7 t^{3} x^{2}) d t + x e^{t^{4}} d x = 0, x (0) = 0

y^{^{'}} = 3 (y - 1)^{\frac{2}{3}}