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Beliebt Rechnen >

y^{''}+3y^'+5y=4t+2+e^{7t}

Lösung

y^{^{''}} + 3 y^{^{'}} + 5 y = 4 t + 2 + e^{7 t}

Lösung

y = e^{- \frac{3 t}{2}} (c_{1} cos (\frac{11 t}{2}) + c_{2} sin (\frac{11 t}{2})) + \frac{4 t}{5} - \frac{2}{25} + \frac{1}{75} e^{7 t}

Schritte zur Lösung

y^{''} (t) + 3 y^{'} (t) + 5 y = 4 t + 2 + e^{7 t}

Solve linear ODE:

y = e^{- \frac{3 t}{2}} (c_{1} cos (\frac{11 t}{2}) + c_{2} sin (\frac{11 t}{2})) + \frac{4 t}{5} - \frac{2}{25} + \frac{1}{75} e^{7 t}

y = e^{- \frac{3 t}{2}} (c_{1} cos (\frac{11 t}{2}) + c_{2} sin (\frac{11 t}{2})) + \frac{4 t}{5} - \frac{2}{25} + \frac{1}{75} e^{7 t}

Graph

Beliebte Beispiele

y^{'''}-y^{''}-16y^'+16y=3-e^x+e^{4x}

y^{^{'''}} - y^{^{''}} - 16 y^{^{'}} + 16 y = 3 - e^{x} + e^{4 x}

linear y^{''}-6y^'+9y=3x^2+4e^{4x}

l in e a r y^{^{''}} - 6 y^{^{'}} + 9 y = 3 x^{2} + 4 e^{4 x}

y^{''}+4y^'+3y=8xe^x-6

y^{^{''}} + 4 y^{^{'}} + 3 y = 8 x e^{x} - 6

y^{''}+3y^'-10y=e^{-5x}

y^{^{''}} + 3 y^{^{'}} - 10 y = e^{- 5 x}

y^{''}-y^'=x^2e^x

y^{^{''}} - y^{^{'}} = x^{2} e^{x}