(dy)/(dx)+(x^2-1)y=-xy^6

Lösung

\frac{d y}{d x} + (x^{2} - 1) y = - x y^{6}

y = 5 \frac{1}{e ^{\frac{5 ( x ^{3} - 3 x )}{3}} \cdot \int 5 e ^{- 5 (\frac{x ^{3}}{3} - x)} x d x}

Schritte zur Lösung

\frac{d y}{d x} + (x^{2} - 1) y = - x y^{6}

Solve Bernoulli ODE:

y = 5 \frac{1}{e ^{\frac{5 ( x ^{3} - 3 x )}{3}} \cdot \int 5 e ^{- 5 (\frac{x ^{3}}{3} - x)} x d x}

y = 5 \frac{1}{e ^{\frac{5 ( x ^{3} - 3 x )}{3}} \cdot \int 5 e ^{- 5 (\frac{x ^{3}}{3} - x)} x d x}

\frac{\partial}{\partial y} (arctan (yz))

e^{- x} (y^{^{'}} - y) = y^{2}

x \to \infty lim (\frac{ln ( 1 + e ^{- x} )}{e ^{- x}})

x \to - 1 lim (3 (2 x - 1)^{2})

\int \frac{3 sin ( x ) + 2 sec ( x )}{tan ( x )} d x