(e^tx+1)dt+(e^t-1)dx=0,x(1)=1

Lösung

(e^{t} x + 1) d t + (e^{t} - 1) d x = 0, x (1) = 1

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

Schritte zur Lösung

(e^{t} x + 1) d t + (e^{t} - 1) d x = 0

Solve exact ODE:

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

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

x \to 1 lim (lo g_{\frac{1}{e}} (x))

l a pl a ce t r an s f or m t \cdot e^{5 t} sin (3 t)

\frac{\partial}{\partial y} (1 - x y)

in v erse l a pl a ce \frac{1}{s ( s ^{2} + 4 )} + 1

x \to 0 lim (\frac{\frac{4}{x - 1} + 4}{x})