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Beliebt Rechnen >

y^{''}-2y^'+2y=cos(t),y(0)=1,y^'(0)=0

Lösung

y^{^{''}} - 2 \cdot y^{^{'}} + 2 \cdot y = cos (t), y (0) = 1, y^{^{'}} (0) = 0

Lösung

y = e^{t} (\frac{4}{5} cos (t) - \frac{2}{5} sin (t)) - \frac{2}{5} sin (t) + \frac{1}{5} cos (t)

Schritte zur Lösung

y^{''} (t) - 2 \cdot y^{'} (t) + 2 \cdot y = cos (t)

Solve linear ODE:

y = e^{t} (\frac{4}{5} cos (t) - \frac{2}{5} sin (t)) - \frac{2}{5} sin (t) + \frac{1}{5} cos (t)

y = e^{t} (\frac{4}{5} cos (t) - \frac{2}{5} sin (t)) - \frac{2}{5} sin (t) + \frac{1}{5} cos (t)

Graph

Beliebte Beispiele

y^{''}+6y=t,y(0)=-3,y^'(0)=0

y^{^{''}} + 6 y = t, y (0) = - 3, y^{^{'}} (0) = 0

3y^{''}+2y^'+1=0

3 y^{^{''}} + 2 y^{^{'}} + 1 = 0

y^{''}-y^'-6y=e^{-3x}(7-8x+6x^2)

y^{^{''}} - y^{^{'}} - 6 y = e^{- 3 x} (7 - 8 x + 6 x^{2})

y^{''}-2y^'+y=e^t,y(0)=0,y^'(0)=9

y^{^{''}} - 2 y^{^{'}} + y = e^{t}, y (0) = 0, y^{^{'}} (0) = 9

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

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