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Beliebt Rechnen >

x^{''}-4x^'+4x=e^t+e^{2t}+1

Lösung

x^{^{''}} - 4 x^{^{'}} + 4 x = e^{t} + e^{2 t} + 1

Lösung

x = c_{1} e^{2 t} + c_{2} t e^{2 t} + e^{t} + \frac{e ^{2 t} t ^{2}}{2} + \frac{1}{4}

Schritte zur Lösung

x^{''} (t) - 4 x^{'} (t) + 4 x = e^{t} + e^{2 t} + 1

Solve linear ODE:

x = c_{1} e^{2 t} + c_{2} t e^{2 t} + e^{t} + \frac{e ^{2 t} t ^{2}}{2} + \frac{1}{4}

x = c_{1} e^{2 t} + c_{2} t e^{2 t} + e^{t} + \frac{e ^{2 t} t ^{2}}{2} + \frac{1}{4}

Graph

Beliebte Beispiele

y^{''}-3y^'+2y=sin(3x),y(0)=1,y^'(0)=0

y^{^{''}} - 3 y^{^{'}} + 2 y = sin (3 x), y (0) = 1, y^{^{'}} (0) = 0

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

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

y^{''}-4y=96x^2e^{2x}+4e^{-2x}

y^{^{''}} - 4 y = 96 x^{2} e^{2 x} + 4 e^{- 2 x}

x^{^{''}} + x^{^{'}} = t

(d^2-1)y=x^2e^x

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