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Beliebt Rechnen >

y^{''}+5y^'=e^{-t},y(0)=0,y^'(0)=1

Lösung

y^{^{''}} + 5 y^{^{'}} = e^{- t}, y (0) = 0, y^{^{'}} (0) = 1

Lösung

y = \frac{3}{20} + \frac{1}{4} - \frac{3}{20} e^{- 5 t} - \frac{1}{4} e^{- t}

Schritte zur Lösung

y^{''} (t) + 5 y^{'} (t) = e^{- t}

Solve linear ODE:

y = \frac{3}{20} + \frac{1}{4} - \frac{3}{20} e^{- 5 t} - \frac{1}{4} e^{- t}

y = \frac{3}{20} + \frac{1}{4} - \frac{3}{20} e^{- 5 t} - \frac{1}{4} e^{- t}

Graph

Beliebte Beispiele

limit as x approaches 4 of f(x)

x \to 4 lim (f (x))

f (x) = - \frac{1}{x}

integral of 1/(x^2+2x+1)

\int \frac{1}{x ^{2} + 2 x + 1} d x

integral of (x^4)/(sqrt(x^2-9))

\int \frac{x ^{4}}{x ^{2} - 9} d x

4x^2y^'=y^'+6xe^{-y}

4 x^{2} y^{^{'}} = y^{^{'}} + 6 x e^{- y}