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Beliebt Rechnen >

y^{''}+3y^'+2y=6e^{-t},y(0)=1,y^'(0)=2

Lösung

y^{^{''}} + 3 y^{^{'}} + 2 y = 6 e^{- t}, y (0) = 1, y^{^{'}} (0) = 2

Lösung

y = - 2 e^{- t} + 3 e^{- 2 t} + 6 e^{- t} t

Schritte zur Lösung

y^{''} (t) + 3 y^{'} (t) + 2 y = 6 e^{- t}

Solve linear ODE:

y = - 2 e^{- t} + 3 e^{- 2 t} + 6 e^{- t} t

y = - 2 e^{- t} + 3 e^{- 2 t} + 6 e^{- t} t

Graph

Beliebte Beispiele

(d^2y)/(dx^2)-(dy)/(dx)+5=0

\frac{d ^{2} y}{d x ^{2}} - \frac{d y}{d x} + 5 = 0

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

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

y^{''}+2y^'+2y=6

y^{^{''}} + 2 y^{^{'}} + 2 y = 6

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

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

y^{''}-8y^'+16y=16x+8

y^{^{''}} - 8 y^{^{'}} + 16 y = 16 x + 8