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Beliebt Rechnen >

y^{''}-4y^'+5y=2e^x

Lösung

y^{^{''}} - 4 y^{^{'}} + 5 y = 2 e^{x}

Lösung

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

Schritte zur Lösung

y^{''} (x) - 4 y^{'} (x) + 5 y = 2 e^{x}

Solve linear ODE:

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

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

Graph

Beliebte Beispiele

y^{''}+2y^'=e^x

y^{^{''}} + 2 y^{^{'}} = e^{x}

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

y^{^{''}} - y = \frac{1}{1 + e ^{x}}

1/2 q^{''}+10q^'+(1/(10^{-2)})q=200

\frac{1}{2} q^{^{''}} + 10 q^{^{'}} + (\frac{1}{1 0 ^{- 2}}) q = 200

y^{'''}+4y^{''}+5y^'=11+5e^{2x}

y^{^{'''}} + 4 y^{^{''}} + 5 y^{^{'}} = 11 + 5 e^{2 x}

y^{''}-3y^'+2y=3e^{-x}

y^{^{''}} - 3 y^{^{'}} + 2 y = 3 e^{- x}