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

Lösung

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

y = \frac{144 x ^{4}}{69 x ^{4} + 92 x ^{2} + 32} + \frac{192 x ^{2}}{69 x ^{4} + 92 x ^{2} + 32} + \frac{64}{69 x ^{4} + 92 x ^{2} + 32}

Schritte zur Lösung

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

Solve separable ODE:

y = \frac{144 x ^{4}}{69 x ^{4} + 92 x ^{2} + 32} + \frac{192 x ^{2}}{69 x ^{4} + 92 x ^{2} + 32} + \frac{64}{69 x ^{4} + 92 x ^{2} + 32}

y = \frac{144 x ^{4}}{69 x ^{4} + 92 x ^{2} + 32} + \frac{192 x ^{2}}{69 x ^{4} + 92 x ^{2} + 32} + \frac{64}{69 x ^{4} + 92 x ^{2} + 32}

\frac{d y}{d t} = 4 (1 - y)^{2}

y + x y^{^{'}} = 9

(1 + e^{x}) y^{^{'}} = y - y e^{x}

\frac{d y}{d x} = \frac{x}{y ^{2}}, y (0) = 2

\frac{d y}{d t} - t y = y, y (1) = 3