(dy)/(dt)=e^t(y-1)^2

Lösung

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

y = - \frac{1}{e ^{t} + c _{1}} + \frac{e ^{t}}{e ^{t} + c _{1}} + \frac{c _{1}}{e ^{t} + c _{1}}

Schritte zur Lösung

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

Solve separable ODE:

y = - \frac{1}{e ^{t} + c _{1}} + \frac{e ^{t}}{e ^{t} + c _{1}} + \frac{c _{1}}{e ^{t} + c _{1}}

y = - \frac{1}{e ^{t} + c _{1}} + \frac{e ^{t}}{e ^{t} + c _{1}} + \frac{c _{1}}{e ^{t} + c _{1}}

x \to 2 lim (\frac{x + 2}{x ^{2} - 4})

\int \frac{1}{x} sin (x) d x

\int (1 + 0.5 t) e^{- 0.004 t} d t

\frac{\partial}{\partial x} (5 x^{2} - 2 y)

\int (x^{\frac{3}{2}} + 8 x + 9) d x