y^5(dy)/(dx)=2x^4y^6-6x^4

Lösung

y^{5} \frac{d y}{d x} = 2 x^{4} y^{6} - 6 x^{4}

y = 6 e^{c_{1} + \frac{12 x ^{5}}{5}} + 33 \cdot 3^{\frac{2}{3}}, y = - 6 e^{c_{1} + \frac{12 x ^{5}}{5}} + 33 \cdot 3^{\frac{2}{3}}

Schritte zur Lösung

y^{5} \frac{d y}{d x} = 2 x^{4} y^{6} - 6 x^{4}

Solve separable ODE:

y = 6 e^{c_{1} + \frac{12 x ^{5}}{5}} + 33 \cdot 3^{\frac{2}{3}}, y = - 6 e^{c_{1} + \frac{12 x ^{5}}{5}} + 33 \cdot 3^{\frac{2}{3}}

y = 6 e^{c_{1} + \frac{12 x ^{5}}{5}} + 33 \cdot 3^{\frac{2}{3}}, y = - 6 e^{c_{1} + \frac{12 x ^{5}}{5}} + 33 \cdot 3^{\frac{2}{3}}

\frac{y ^{2} d y}{d x} = x

(x^{2} + 1) (\frac{d y}{d x}) + 3 x (y - 1) = 0, y (0) = 5

y^{^{'}} - 2 t y = - t, y (0) = \frac{15}{2}

x^{3} d x + (y + 1) d y = 0

2 x y y^{^{'}} = x + 3