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Beliebt Rechnen >

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

Lösung

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

Lösung

y = e^{x} (c_{1} cos (2 x) + c_{2} sin (2 x)) + \frac{1}{5} e^{2 x}

Schritte zur Lösung

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

Solve linear ODE:

y = e^{x} (c_{1} cos (2 x) + c_{2} sin (2 x)) + \frac{1}{5} e^{2 x}

y = e^{x} (c_{1} cos (2 x) + c_{2} sin (2 x)) + \frac{1}{5} e^{2 x}

Graph

Beliebte Beispiele

y^{''''}+2y^{''}+y=3t+4

y^{^{''''}} + 2 y^{^{''}} + y = 3 t + 4

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

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

4y^{''}-4y^'+y=32e^{t/2}

4 y^{^{''}} - 4 y^{^{'}} + y = 32 e^{\frac{t}{2}}

y^{'''}+6y^{''}+9y^'=6x+2

y^{^{'''}} + 6 y^{^{''}} + 9 y^{^{'}} = 6 x + 2

y^{'''}-6y^{''}+12y^'-8y=t^3e^{2t}+1

y^{^{'''}} - 6 y^{^{''}} + 12 y^{^{'}} - 8 y = t^{3} e^{2 t} + 1