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Beliebt Rechnen >

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

Lösung

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

Lösung

y = c_{1} e^{2 x} + c_{2} x e^{2 x} + \frac{e ^{2 x} x ^{4}}{12}

Schritte zur Lösung

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

Solve linear ODE:

y = c_{1} e^{2 x} + c_{2} x e^{2 x} + \frac{e ^{2 x} x ^{4}}{12}

y = c_{1} e^{2 x} + c_{2} x e^{2 x} + \frac{e ^{2 x} x ^{4}}{12}

Graph

Beliebte Beispiele

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

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

x^{''}+2x^'+5x=1,x(0)=0,x^'(0)=0

x^{^{''}} + 2 x^{^{'}} + 5 x = 1, x (0) = 0, x^{^{'}} (0) = 0

y^{''}+9y=e^{-2x}

y^{^{''}} + 9 y = e^{- 2 x}

y^{'''}+3y^{''}+2y^'=x^2+4x+8

y^{^{'''}} + 3 y^{^{''}} + 2 y^{^{'}} = x^{2} + 4 x + 8

y^{''}+4y^'+4y=-2sin(3x)

y^{^{''}} + 4 y^{^{'}} + 4 y = - 2 sin (3 x)