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Beliebt Rechnen >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Solve linear ODE:

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

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

Graph

Beliebte Beispiele

6y^{''}+y^'-y=-25e^{2x}+7e^{-2x}

6 y^{^{''}} + y^{^{'}} - y = - 25 e^{2 x} + 7 e^{- 2 x}

(d^3-3d-2)y=x^2

(d^{3} - 3 d - 2) y = x^{2}

y^{''}-3y^'-4=-8e^tcos(2t)

y^{^{''}} - 3 y^{^{'}} - 4 = - 8 e^{t} cos (2 t)

y^{''}-64y=-192t+128t^2

y^{^{''}} - 64 y = - 192 t + 128 t^{2}

y^{'''}-5y^{''}+6y^'=2x+3e^{2x}

y^{^{'''}} - 5 y^{^{''}} + 6 y^{^{'}} = 2 x + 3 e^{2 x}