y^'=y(xy^6+2)

Lösung

y^{^{'}} = y (x y^{6} + 2)

y = 6 \frac{24 e ^{12 x}}{- 12 x e ^{12 x} + e ^{12 x} + c _{1}}, y = - 6 \frac{24 e ^{12 x}}{- 12 x e ^{12 x} + e ^{12 x} + c _{1}}

Schritte zur Lösung

y^{'} (x) = y (x y^{6} + 2)

Solve Bernoulli ODE:

y = 6 \frac{24 e ^{12 x}}{- 12 x e ^{12 x} + e ^{12 x} + c _{1}}, y = - 6 \frac{24 e ^{12 x}}{- 12 x e ^{12 x} + e ^{12 x} + c _{1}}

y = 6 \frac{24 e ^{12 x}}{- 12 x e ^{12 x} + e ^{12 x} + c _{1}}, y = - 6 \frac{24 e ^{12 x}}{- 12 x e ^{12 x} + e ^{12 x} + c _{1}}

y^{^{'}} = \frac{4 t ^{3} + 1}{2 y - 6}

\frac{\partial}{\partial y} (x^{2} y^{3} - \frac{1}{1 + 9 x ^{2}})

t an g e n t f (x) = \frac{6}{x - 1}, at x = 3

d er i v a t i v e f (x) = (16 x)^{3}

f^{^{'}} (x) = 5 x^{4}