(dy)/(dt)=(3t^2+te^{-t}+1)/(2y-4)

Lösung

\frac{d y}{d t} = \frac{3 t ^{2} + t e ^{- t} + 1}{2 y - 4}

y = 2 + t^{3} + t - e^{- t} t - e^{- t} + c_{1} + 4, y = 2 - t^{3} + t - e^{- t} t - e^{- t} + c_{1} + 4

Schritte zur Lösung

\frac{d y}{d t} = \frac{3 t ^{2} + t e ^{- t} + 1}{2 y - 4}

Solve separable ODE:

y = 2 + t^{3} + t - e^{- t} t - e^{- t} + c_{1} + 4, y = 2 - t^{3} + t - e^{- t} t - e^{- t} + c_{1} + 4

y = 2 + t^{3} + t - e^{- t} t - e^{- t} + c_{1} + 4, y = 2 - t^{3} + t - e^{- t} t - e^{- t} + c_{1} + 4

\int \frac{a}{x ^{2}} d x

\int \frac{1}{( x + 3 )} d x

\frac{d}{d x} (\frac{( 3 - 2 x - x ^{2} )}{( x ^{2} - 1 )})

\frac{d y}{d t} = y \cdot ln (t), y (e) = 200

x \to 2 lim (\frac{- x}{( 2 - x )})