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Beliebt Rechnen >

y^{''}-4y^'+5y=e^{-3t},y(0)=1,y^'(0)=0

Lösung

y^{^{''}} - 4 y^{^{'}} + 5 y = e^{- 3 t}, y (0) = 1, y^{^{'}} (0) = 0

Lösung

y = e^{2 t} (\frac{25}{26} cos (t) - \frac{47}{26} sin (t)) + \frac{1}{26} e^{- 3 t}

Schritte zur Lösung

y^{''} (t) - 4 y^{'} (t) + 5 y = e^{- 3 t}

Solve linear ODE:

y = e^{2 t} (\frac{25}{26} cos (t) - \frac{47}{26} sin (t)) + \frac{1}{26} e^{- 3 t}

y = e^{2 t} (\frac{25}{26} cos (t) - \frac{47}{26} sin (t)) + \frac{1}{26} e^{- 3 t}

Graph

Beliebte Beispiele

(d^2y)/(dx^2)+100y=csc(10x)

\frac{d ^{2} y}{d x ^{2}} + 100 y = csc (10 x)

y^{''}+y^'+y=x^4+4x^3+12x^2

y^{^{''}} + y^{^{'}} + y = x^{4} + 4 x^{3} + 12 x^{2}

(D^2+5D+6)y=(D+1)x

(D^{2} + 5 D + 6) y = (D + 1) x

y^{''}+4y^'=2sec^3(2t)

y^{^{''}} + 4 y^{^{'}} = 2 sec^{3} (2 t)

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

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