(x+y)^2dx+(2xy+x^2-6)dy=0,y(1)=1

解

(x + y)^{2} d x + (2 x y + x^{2} - 6) d y = 0, y (1) = 1

y = \frac{18 - 3 x ^{2} + 324 - 108 x ^{2} - 3 x ^{4} + 36 c _{1} x}{6 x}, y = \frac{18 - 3 x ^{2} - 324 - 108 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} - 6) d y = 0

完全 ODE を解く:

y = \frac{18 - 3 x ^{2} + 324 - 108 x ^{2} - 3 x ^{4} + 36 c _{1} x}{6 x}, y = \frac{18 - 3 x ^{2} - 324 - 108 x ^{2} - 3 x ^{4} + 36 c _{1} x}{6 x}

y = \frac{18 - 3 x ^{2} + 324 - 108 x ^{2} - 3 x ^{4} + 36 c _{1} x}{6 x}, y = \frac{18 - 3 x ^{2} - 324 - 108 x ^{2} - 3 x ^{4} + 36 c _{1} x}{6 x}