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Beliebt Rechnen >

y^{''}+4y^'+20y=4cos(2x)

Lösung

y^{^{''}} + 4 y^{^{'}} + 20 y = 4 cos (2 x)

Lösung

y = e^{- 2 x} (c_{1} cos (4 x) + c_{2} sin (4 x)) + \frac{1}{10} sin (2 x) + \frac{1}{5} cos (2 x)

Schritte zur Lösung

y^{''} (x) + 4 y^{'} (x) + 20 y = 4 cos (2 x)

Solve linear ODE:

y = e^{- 2 x} (c_{1} cos (4 x) + c_{2} sin (4 x)) + \frac{1}{10} sin (2 x) + \frac{1}{5} cos (2 x)

y = e^{- 2 x} (c_{1} cos (4 x) + c_{2} sin (4 x)) + \frac{1}{10} sin (2 x) + \frac{1}{5} cos (2 x)

Graph

Beliebte Beispiele

7y^{''}+5y^'-y=9

7 y^{^{''}} + 5 y^{^{'}} - y = 9

y^{''}+3y^'+2.25y=9t^3+64,y(0)=1,y^'(0)=31.5

y^{^{''}} + 3 y^{^{'}} + 2.25 y = 9 t^{3} + 64, y (0) = 1, y^{^{'}} (0) = 31.5

y^{''}+3y^'-4y=-32t^2

y^{^{''}} + 3 y^{^{'}} - 4 y = - 32 t^{2}

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

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

y^{''}+3y+2=0,y(2)=-1,y^'(0)=0

y^{^{''}} + 3 y + 2 = 0, y (2) = - 1, y^{^{'}} (0) = 0