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Beliebt Rechnen >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Solve linear ODE:

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

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

Graph

Beliebte Beispiele

y^{''}-3y^'+5y=24e^{-2x}

y^{^{''}} - 3 y^{^{'}} + 5 y = 24 e^{- 2 x}

x^{''}+5x^'+6x=2e^{-t}

x^{^{''}} + 5 x^{^{'}} + 6 x = 2 e^{- t}

y^{''}+y^'-2y=2xe^{2x}

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

y^{''}-7y^'+12=0

y^{^{''}} - 7 y^{^{'}} + 12 = 0

y^{''}-2y^'-3=0

y^{^{''}} - 2 y^{^{'}} - 3 = 0