(dy)/(dt)+e^ty=-5e^t

Lösung

\frac{d y}{d t} + e^{t} y = - 5 e^{t}

y = e^{- e^{t} + c_{1}} - 5

Schritte zur Lösung

\frac{d y}{d t} + e^{t} y = - 5 e^{t}

Solve separable ODE:

y = e^{- e^{t} + c_{1}} - 5

y = e^{- e^{t} + c_{1}} - 5

\int x^{2} y cos (x) + 2 x y sin (x) - y^{2} e^{x} d x

\int (\frac{1}{( 25 - x ^{2} ) ^{\frac{3}{2}}}) d x

\int \frac{5 + x}{5 - x} d x

\int \frac{e ^{x} + 1}{x} d x

t an g e n t f (x) = \frac{4}{x + 1}, at x = 1