y^'=(6yx^2)/(x^3+1)

Lösung

y^{^{'}} = \frac{6 y x ^{2}}{x ^{3} + 1}

y = e^{c_{1}} x^{6} + 2 e^{c_{1}} x^{3} + e^{c_{1}}

Schritte zur Lösung

y^{'} (x) = \frac{6 y x ^{2}}{x ^{3} + 1}

Solve separable ODE:

y = e^{c_{1}} x^{6} + 2 e^{c_{1}} x^{3} + e^{c_{1}}

y = e^{c_{1}} x^{6} + 2 e^{c_{1}} x^{3} + e^{c_{1}}

\frac{d y}{d x} = \frac{6 y}{x}, x > 0

y^{^{'}} = 3 \frac{y}{x - 1}

y^{^{'}} + 6 y = 4, y (0) = 0

\frac{d y}{d x} = \frac{( ln ( x ) ) ^{6}}{x y ^{2}}

y^{^{'}} + 5 y^{3} = 0