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Beliebt Rechnen >

x^{''}-4x^'+4x=e^{2t}

Lösung

x^{^{''}} - 4 x^{^{'}} + 4 x = e^{2 t}

Lösung

x = c_{1} e^{2 t} + c_{2} t e^{2 t} + \frac{e ^{2 t} t ^{2}}{2}

Schritte zur Lösung

x^{''} (t) - 4 x^{'} (t) + 4 x = e^{2 t}

Solve linear ODE:

x = c_{1} e^{2 t} + c_{2} t e^{2 t} + \frac{e ^{2 t} t ^{2}}{2}

x = c_{1} e^{2 t} + c_{2} t e^{2 t} + \frac{e ^{2 t} t ^{2}}{2}

Graph

Beliebte Beispiele

y^{''}+4y=4cos(2x)+6cos(x)+8x^2-4x

y^{^{''}} + 4 y = 4 cos (2 x) + 6 cos (x) + 8 x^{2} - 4 x

y^{''}-4y^'+3y=20cos(x)

y^{^{''}} - 4 y^{^{'}} + 3 y = 20 cos (x)

x^{''}+x^'+12x=20cos(3t)

x^{^{''}} + x^{^{'}} + 12 x = 20 cos (3 t)

y^{''}+6y^'+9y=2e^{-3t}

y^{^{''}} + 6 y^{^{'}} + 9 y = 2 e^{- 3 t}

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

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