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Beliebt Rechnen >

y^{''}-5y^'+4y=3e^xsin(x)

Lösung

y^{^{''}} - 5 y^{^{'}} + 4 y = 3 e^{x} sin (x)

Lösung

y = c_{1} e^{4 x} + c_{2} e^{x} + \frac{9}{10} e^{x} cos (x) - \frac{3}{10} e^{x} sin (x)

Schritte zur Lösung

y^{''} (x) - 5 y^{'} (x) + 4 y = 3 e^{x} sin (x)

Solve linear ODE:

y = c_{1} e^{4 x} + c_{2} e^{x} + \frac{9}{10} e^{x} cos (x) - \frac{3}{10} e^{x} sin (x)

y = c_{1} e^{4 x} + c_{2} e^{x} + \frac{9}{10} e^{x} cos (x) - \frac{3}{10} e^{x} sin (x)

Graph

Beliebte Beispiele

y^{''}-4y^'+4y=e^{2x}(12x^2-6x)

y^{^{''}} - 4 y^{^{'}} + 4 y = e^{2 x} (12 x^{2} - 6 x)

y^{'''}-3y^{''}+3y^'=x-8e^x

y^{^{'''}} - 3 y^{^{''}} + 3 y^{^{'}} = x - 8 e^{x}

y^{'''}-y^{''}-16y^'+16y=9-e^x+e^{4x}

y^{^{'''}} - y^{^{''}} - 16 y^{^{'}} + 16 y = 9 - e^{x} + e^{4 x}

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

(d^2-1)y=e^x+4e^{-x}

(d^{2} - 1) y = e^{x} + 4 e^{- x}