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Beliebt Rechnen >

y^{''}-2y^'+2y=e^{-t},y(0)=0,y^'(0)=7

Lösung

y^{^{''}} - 2 y^{^{'}} + 2 y = e^{- t}, y (0) = 0, y^{^{'}} (0) = 7

Lösung

y = e^{t} (- \frac{1}{5} cos (t) + \frac{37}{5} sin (t)) + \frac{1}{5} e^{- t}

Schritte zur Lösung

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

Solve linear ODE:

y = e^{t} (- \frac{1}{5} cos (t) + \frac{37}{5} sin (t)) + \frac{1}{5} e^{- t}

y = e^{t} (- \frac{1}{5} cos (t) + \frac{37}{5} sin (t)) + \frac{1}{5} e^{- t}

Graph

Beliebte Beispiele

(d^2y)/(dx^2)+y=4x

\frac{d ^{2} y}{d x ^{2}} + y = 4 x

y^{''}+5y^'+6y=1+e^{-t}

y^{^{''}} + 5 y^{^{'}} + 6 y = 1 + e^{- t}

y^{''}+2y^'-8=0

y^{^{''}} + 2 y^{^{'}} - 8 = 0

0.5q^{''}+20q^'+1/(0.0025)q=100

0.5 q^{^{''}} + 20 q^{^{'}} + \frac{1}{0.0025} q = 100

x^{''}+16x=14cos(3t)

x^{^{''}} + 16 x = 14 cos (3 t)