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Beliebt Rechnen >

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

Lösung

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

Lösung

y = e^{t} (- \frac{1}{5} cos (t) + \frac{17}{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{17}{5} sin (t)) + \frac{1}{5} e^{- t}

y = e^{t} (- \frac{1}{5} cos (t) + \frac{17}{5} sin (t)) + \frac{1}{5} e^{- t}

Graph

Beliebte Beispiele

y^{''}-5y^'-6y=10,y(0)=2,y^'(0)=1

y^{^{''}} - 5 y^{^{'}} - 6 y = 10, y (0) = 2, y^{^{'}} (0) = 1

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

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

y^{''}+y^'=sec(t)

y^{^{''}} + y^{^{'}} = sec (t)

(d^2y)/(dx^2)+y=-1

\frac{d ^{2} y}{d x ^{2}} + y = - 1

y^{''}+4y=(sin(x))^2

y^{^{''}} + 4 y = (sin (x))^{2}