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Beliebt Rechnen >

y^{''}-y^'=e^{-3t},y(0)=0,y^'(0)=0

Lösung

y^{^{''}} - y^{^{'}} = e^{- 3 t}, y (0) = 0, y^{^{'}} (0) = 0

Lösung

y = (\frac{1}{3} - \frac{1}{12}) e^{t} - \frac{1}{3} + \frac{1}{12} e^{- 3 t}

Schritte zur Lösung

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

Solve linear ODE:

y = (\frac{1}{3} - \frac{1}{12}) e^{t} - \frac{1}{3} + \frac{1}{12} e^{- 3 t}

y = (\frac{1}{3} - \frac{1}{12}) e^{t} - \frac{1}{3} + \frac{1}{12} e^{- 3 t}

Graph

Beliebte Beispiele

y^{''}+8y^'+16=0,y(0)=1,y^'(0)=0

y^{^{''}} + 8 y^{^{'}} + 16 = 0, y (0) = 1, y^{^{'}} (0) = 0

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

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

y^{''}-4y^'+4y=15sin(x)-35cos(x)

y^{^{''}} - 4 y^{^{'}} + 4 y = 15 sin (x) - 35 cos (x)

y^{''}+3y^'+2y=2x+x^2

y^{^{''}} + 3 y^{^{'}} + 2 y = 2 x + x^{2}

y^{''}-a^2*y+b=0

y^{^{''}} - a^{2} \cdot y + b = 0