xd3ydx3-(dydx)4+y=0

解答

x d 3 y d x 3 - (d y d x) 4 + y = 0

y = 0, x = \frac{2 d + 4 d ^{2} - 9}{9 d}, x = \frac{2 d - 4 d ^{2} - 9}{9 d}; d \neq = 0

求解步骤

x d \cdot 3 y d x \cdot 3 - (d y d x) \cdot 4 + y = 0

分解

x d \cdot 3 y d x \cdot 3 - (d y d x) \cdot 4 + y : y (1 + 9 d^{2} x^{2} - 4 d^{2} x)

y (1 + 9 d^{2} x^{2} - 4 d^{2} x) = 0

使用零因数法则： If

ab = 0

then

a = 0

b = 0

y = 0 or 1 + 9 d^{2} x^{2} - 4 d^{2} x = 0

y = 0

解

1 + 9 d^{2} x^{2} - 4 d^{2} x = 0 : x = \frac{2 d + 4 d ^{2} - 9}{9 d}, x = \frac{2 d - 4 d ^{2} - 9}{9 d}; d \neq = 0

解为

y = 0, x = \frac{2 d + 4 d ^{2} - 9}{9 d}, x = \frac{2 d - 4 d ^{2} - 9}{9 d}; d \neq = 0

co x = 0

∣ x - 1 ∣ (y + 2)^{2022} = 0

2 x (y + 1)^{2} = 0, 2 x^{2} (y + 1) = 0

(1 + z^{6}) (x) = 0

so l v e f or y, 6 x y - 12 x = 0.3 x^{2} + 3 y^{2} - 12 y