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Beliebt Rechnen >

y^{''}-y=2e^{-t},y(0)=0,y^'(0)=0

Lösung

y^{^{''}} - y = 2 e^{- t}, y (0) = 0, y^{^{'}} (0) = 0

Lösung

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

Schritte zur Lösung

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

Solve linear ODE:

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

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

Graph

Beliebte Beispiele

2y^{''}+3y^'-2y=10x^2-4x-15

2 y^{^{''}} + 3 y^{^{'}} - 2 y = 10 x^{2} - 4 x - 15

x^{'''}+10x^{''}+33x^'+36x=4te^{-3t}

x^{^{'''}} + 10 x^{^{''}} + 33 x^{^{'}} + 36 x = 4 t e^{- 3 t}

y^{''}-6y^'+9y=12e^tsin(t)

y^{^{''}} - 6 y^{^{'}} + 9 y = 12 e^{t} sin (t)

y^{''}+4y=-16sin(2t)

y^{^{''}} + 4 y = - 16 sin (2 t)

y^{''}+4y^'+13y=52,y(0)=2,y^'(0)=1

y^{^{''}} + 4 y^{^{'}} + 13 y = 52, y (0) = 2, y^{^{'}} (0) = 1