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

Lösung

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

y = 6 e^{c_{1} + \frac{12 x ^{5}}{5}} + 32 \cdot 2^{\frac{2}{3}}, y = - 6 e^{c_{1} + \frac{12 x ^{5}}{5}} + 32 \cdot 2^{\frac{2}{3}}

Schritte zur Lösung

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

Solve separable ODE:

y = 6 e^{c_{1} + \frac{12 x ^{5}}{5}} + 32 \cdot 2^{\frac{2}{3}}, y = - 6 e^{c_{1} + \frac{12 x ^{5}}{5}} + 32 \cdot 2^{\frac{2}{3}}

y = 6 e^{c_{1} + \frac{12 x ^{5}}{5}} + 32 \cdot 2^{\frac{2}{3}}, y = - 6 e^{c_{1} + \frac{12 x ^{5}}{5}} + 32 \cdot 2^{\frac{2}{3}}

\frac{d y}{d x} = 4 x^{4} y

4 y - 5 x y^{^{'}} = 0

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

y^{^{'}} = 6 x y^{8}

\frac{d y}{d t} = - 2 y + 5