(x+y)^2dx+(2xy+x^2-2)dy=0

解

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

y = \frac{6 - 3 x ^{2} + 36 - 36 x ^{2} - 3 x ^{4} + 36 c _{1} x}{6 x}, y = \frac{6 - 3 x ^{2} - 36 - 36 x ^{2} - 3 x ^{4} + 36 c _{1} x}{6 x}

解答ステップ

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

完全 ODE を解く:

y = \frac{6 - 3 x ^{2} + 36 - 36 x ^{2} - 3 x ^{4} + 36 c _{1} x}{6 x}, y = \frac{6 - 3 x ^{2} - 36 - 36 x ^{2} - 3 x ^{4} + 36 c _{1} x}{6 x}

y = \frac{6 - 3 x ^{2} + 36 - 36 x ^{2} - 3 x ^{4} + 36 c _{1} x}{6 x}, y = \frac{6 - 3 x ^{2} - 36 - 36 x ^{2} - 3 x ^{4} + 36 c _{1} x}{6 x}