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Beliebt Rechnen >

y^{''}+4y=8sin(2t)+5e^t

Lösung

y^{^{''}} + 4 y = 8 sin (2 t) + 5 e^{t}

Lösung

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

Schritte zur Lösung

y^{''} (t) + 4 y = 8 sin (2 t) + 5 e^{t}

Solve linear ODE:

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

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

Graph

Beliebte Beispiele

y^{''}-8y^'+16y=2e^{4x}

y^{^{''}} - 8 y^{^{'}} + 16 y = 2 e^{4 x}

y^{''}+4y^'+4y=e^xcos(x)

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

y^{''}+4y^'+13y=5cos(2t)

y^{^{''}} + 4 y^{^{'}} + 13 y = 5 cos (2 t)

x^{''}-6x^'+10x=30t

x^{^{''}} - 6 x^{^{'}} + 10 x = 30 t

y^{''}-y^'-12y=(x+1)e^x

y^{^{''}} - y^{^{'}} - 12 y = (x + 1) e^{x}