(4x^3+4xy-1)dx=(1-2x^2-2y)dy

解

(4 x^{3} + 4 x y - 1) d x = (1 - 2 x^{2} - 2 y) d y

y = \frac{1 - 2 x ^{2} + 1 - 4 x ^{2} + 4 x + c _{1}}{2}, y = \frac{1 - 2 x ^{2} - 1 - 4 x ^{2} + 4 x + c _{1}}{2}

解答ステップ

(4 x^{3} + 4 x y - 1) d x = (1 - 2 x^{2} - 2 y) d y

完全 ODE を解く:

y = \frac{1 - 2 x ^{2} + 1 - 4 x ^{2} + 4 x + c _{1}}{2}, y = \frac{1 - 2 x ^{2} - 1 - 4 x ^{2} + 4 x + c _{1}}{2}

y = \frac{1 - 2 x ^{2} + 1 - 4 x ^{2} + 4 x + c _{1}}{2}, y = \frac{1 - 2 x ^{2} - 1 - 4 x ^{2} + 4 x + c _{1}}{2}