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Beliebt Rechnen >

y^{''}-4y^'+4y=12te^{2t}(t+1)

Lösung

y^{^{''}} - 4 y^{^{'}} + 4 y = 12 t e^{2 t} (t + 1)

Lösung

y = c_{1} e^{2 t} + c_{2} t e^{2 t} + e^{2 t} t^{4} + 2 e^{2 t} t^{3}

Schritte zur Lösung

y^{''} (t) - 4 y^{'} (t) + 4 y = 12 t e^{2 t} (t + 1)

Solve linear ODE:

y = c_{1} e^{2 t} + c_{2} t e^{2 t} + e^{2 t} t^{4} + 2 e^{2 t} t^{3}

y = c_{1} e^{2 t} + c_{2} t e^{2 t} + e^{2 t} t^{4} + 2 e^{2 t} t^{3}

Graph

Beliebte Beispiele

y^{''}-5y^'+6y=4e^{4x},y(0)=0,y^'(0)=1

y^{^{''}} - 5 y^{^{'}} + 6 y = 4 e^{4 x}, y (0) = 0, y^{^{'}} (0) = 1

(d^2+4)y=cos(2x)

(d^{2} + 4) y = cos (2 x)

y^{''}-14y^'+49y=21x+2

y^{^{''}} - 14 y^{^{'}} + 49 y = 21 x + 2

y^{''}+4y^'+5y=-15x+3e^{-x}

y^{^{''}} + 4 y^{^{'}} + 5 y = - 15 x + 3 e^{- x}

y^{''}+y^'=cos(2x)+e^x+x^2

y^{^{''}} + y^{^{'}} = cos (2 x) + e^{x} + x^{2}