(3x^2+2)^3y^'-xy^2=0,y(0)= 3/2

解

(3 x^{2} + 2)^{3} y^{^{'}} - x y^{2} = 0, y (0) = \frac{3}{2}

y = \frac{432 x ^{4}}{279 x ^{4} + 372 x ^{2} + 128} + \frac{576 x ^{2}}{279 x ^{4} + 372 x ^{2} + 128} + \frac{192}{279 x ^{4} + 372 x ^{2} + 128}

解答ステップ

(3 x^{2} + 2)^{3} y^{'} (x) - x y^{2} = 0

分離可能 ODE を解く:

y = \frac{432 x ^{4}}{279 x ^{4} + 372 x ^{2} + 128} + \frac{576 x ^{2}}{279 x ^{4} + 372 x ^{2} + 128} + \frac{192}{279 x ^{4} + 372 x ^{2} + 128}

y = \frac{432 x ^{4}}{279 x ^{4} + 372 x ^{2} + 128} + \frac{576 x ^{2}}{279 x ^{4} + 372 x ^{2} + 128} + \frac{192}{279 x ^{4} + 372 x ^{2} + 128}