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Beliebt Rechnen >

y^{''}+6y^'+5y=10cos(5t)

Lösung

y^{^{''}} + 6 y^{^{'}} + 5 y = 10 cos (5 t)

Lösung

y = c_{1} e^{- t} + c_{2} e^{- 5 t} + \frac{3}{13} sin (5 t) - \frac{2}{13} cos (5 t)

Schritte zur Lösung

y^{''} (t) + 6 y^{'} (t) + 5 y = 10 cos (5 t)

Solve linear ODE:

y = c_{1} e^{- t} + c_{2} e^{- 5 t} + \frac{3}{13} sin (5 t) - \frac{2}{13} cos (5 t)

y = c_{1} e^{- t} + c_{2} e^{- 5 t} + \frac{3}{13} sin (5 t) - \frac{2}{13} cos (5 t)

Graph

Beliebte Beispiele

y^{''}-4y^'-12y=sin(3t)

y^{^{''}} - 4 y^{^{'}} - 12 y = sin (3 t)

y^{''}+9y=sin(3x)+e^{2x}

y^{^{''}} + 9 y = sin (3 x) + e^{2 x}

y^{''}-y^'-2y=8x+5

y^{^{''}} - y^{^{'}} - 2 y = 8 x + 5

y^{''}-2y^'-3y=2e^{3t}

y^{^{''}} - 2 y^{^{'}} - 3 y = 2 e^{3 t}

y^{''}-4y^'+4y=e^2xln(x)

y^{^{''}} - 4 y^{^{'}} + 4 y = e^{2} x ln (x)