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Beliebt Rechnen >

2y^{''}-y^'-2y=2e^{-t}

Lösung

2 y^{^{''}} - y^{^{'}} - 2 y = 2 e^{- t}

Lösung

y = c_{1} e^{\frac{( 1 + 17 ) t}{4}} + c_{2} e^{\frac{( 1 - 17 ) t}{4}} + 2 e^{- t}

Schritte zur Lösung

2 y^{''} (t) - y^{'} (t) - 2 y = 2 e^{- t}

Solve linear ODE:

y = c_{1} e^{\frac{( 1 + 17 ) t}{4}} + c_{2} e^{\frac{( 1 - 17 ) t}{4}} + 2 e^{- t}

y = c_{1} e^{\frac{( 1 + 17 ) t}{4}} + c_{2} e^{\frac{( 1 - 17 ) t}{4}} + 2 e^{- t}

Graph

Beliebte Beispiele

y^{''}+4y=20e^t,y(0)=0,y^'(0)=2

y^{^{''}} + 4 y = 20 e^{t}, y (0) = 0, y^{^{'}} (0) = 2

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

y^{''}-15y^'+54y=39+54x

y^{^{''}} - 15 y^{^{'}} + 54 y = 39 + 54 x

x^{''}+3x^'+2x=1,x(0)=0,x^'(0)=0

x^{^{''}} + 3 x^{^{'}} + 2 x = 1, x (0) = 0, x^{^{'}} (0) = 0

y^{^{''}} - 9 y = 54 t