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Beliebt Rechnen >

x^{''}+2x^'+5x=1,x^'(0)=0,x(0)=0

Lösung

x^{^{''}} + 2 x^{^{'}} + 5 x = 1, x^{^{'}} (0) = 0, x (0) = 0

Lösung

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

Schritte zur Lösung

x^{''} (t) + 2 x^{'} (t) + 5 x = 1

Solve linear ODE:

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

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

Graph

Beliebte Beispiele

y^{''}-5y^'=3cos(x)

y^{^{''}} - 5 y^{^{'}} = 3 cos (x)

y^{''}-2y^'+2y=e^2x(cos(x)-8sin(x))

y^{^{''}} - 2 y^{^{'}} + 2 y = e^{2} x (cos (x) - 8 sin (x))

y^{''}-4y=6cos(3x+30)

y^{^{''}} - 4 y = 6 cos (3 x + 3 0^{\circ})

y^{'''}+y^{''}+y^'=e^x

y^{^{'''}} + y^{^{''}} + y^{^{'}} = e^{x}

y^{''}-8y^'+16y=2e^{4x}+3cos(4x)-2x+1

y^{^{''}} - 8 y^{^{'}} + 16 y = 2 e^{4 x} + 3 cos (4 x) - 2 x + 1