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Beliebt Rechnen >

ay^{''}+2y^'=4e^{2t},y(0)=0,y^'(0)=0

Lösung

a y^{^{''}} + 2 y^{^{'}} = 4 e^{2 t}, y (0) = 0, y^{^{'}} (0) = 0

Lösung

y = - \frac{a}{a + 1} - \frac{1}{a + 1} + \frac{a e ^{- \frac{2 t}{a}}}{a + 1} + \frac{e ^{2 t}}{a + 1}

Schritte zur Lösung

a y^{''} (t) + 2 y^{'} (t) = 4 e^{2 t}

Solve linear ODE:

y = - \frac{a}{a + 1} - \frac{1}{a + 1} + \frac{a e ^{- \frac{2 t}{a}}}{a + 1} + \frac{e ^{2 t}}{a + 1}

y = - \frac{a}{a + 1} - \frac{1}{a + 1} + \frac{a e ^{- \frac{2 t}{a}}}{a + 1} + \frac{e ^{2 t}}{a + 1}

Graph

Beliebte Beispiele

(D^{2} + 3 D) y = - 18 x

y^{''}-2y^'-8y=4e^2-21e^{-3x}

y^{^{''}} - 2 y^{^{'}} - 8 y = 4 e^{2} - 21 e^{- 3 x}

y^{''}+3y^'=e^{-3t}

y^{^{''}} + 3 y^{^{'}} = e^{- 3 t}

(y^{''})+y=3xsin(x)

(y^{^{''}}) + y = 3 x sin (x)

y^{''}+500y^'+20000y=1100

y^{^{''}} + 500 y^{^{'}} + 20000 y = 1100