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Beliebt Rechnen >

y^{''}+0.5y^'+y=cos(t)

Lösung

y^{^{''}} + 0.5 y^{^{'}} + y = cos (t)

Lösung

y = e^{- \frac{t}{4}} (c_{1} cos (\frac{15 t}{4}) + c_{2} sin (\frac{15 t}{4})) + 2 sin (t)

Schritte zur Lösung

y^{''} (t) + 0.5 y^{'} (t) + y = cos (t)

Solve linear ODE:

y = e^{- \frac{t}{4}} (c_{1} cos (\frac{15 t}{4}) + c_{2} sin (\frac{15 t}{4})) + 2 sin (t)

y = e^{- \frac{t}{4}} (c_{1} cos (\frac{15 t}{4}) + c_{2} sin (\frac{15 t}{4})) + 2 sin (t)

Graph

Beliebte Beispiele

y^{''}+y=2cos(x),y(0)=1,y^'(0)=0

y^{^{''}} + y = 2 cos (x), y (0) = 1, y^{^{'}} (0) = 0

y^{''}-3y^'+y=2sin(2x)

y^{^{''}} - 3 y^{^{'}} + y = 2 sin (2 x)

(D+1)^3y=16(2x+3)^{-1}e^x

(D + 1)^{3} y = 16 (2 x + 3)^{- 1} e^{x}

y^{''}-4y^'-8y=8x^2+8x+1

y^{^{''}} - 4 y^{^{'}} - 8 y = 8 x^{2} + 8 x + 1

y^{^{''}} - 9 y = 63