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Beliebt Rechnen >

y^{''}-4y^'+4y=2e^{2x}+4x-12

Lösung

y^{^{''}} - 4 y^{^{'}} + 4 y = 2 e^{2 x} + 4 x - 12

Lösung

y = c_{1} e^{2 x} + c_{2} x e^{2 x} + e^{2 x} x^{2} + x - 2

Schritte zur Lösung

y^{''} (x) - 4 y^{'} (x) + 4 y = 2 e^{2 x} + 4 x - 12

Solve linear ODE:

y = c_{1} e^{2 x} + c_{2} x e^{2 x} + e^{2 x} x^{2} + x - 2

y = c_{1} e^{2 x} + c_{2} x e^{2 x} + e^{2 x} x^{2} + x - 2

Graph

Beliebte Beispiele

y^{''}+y-5=e^{2x}-3+cos(3x)

y^{^{''}} + y - 5 = e^{2 x} - 3 + cos (3 x)

y^{''}+5y^'=-6e^{-5x}

y^{^{''}} + 5 y^{^{'}} = - 6 e^{- 5 x}

y^{''}+2y^'+4y=3sin(5t)

y^{^{''}} + 2 y^{^{'}} + 4 y = 3 sin (5 t)

y^{''}-4y^'-12y=3cos(x)

y^{^{''}} - 4 y^{^{'}} - 12 y = 3 cos (x)

y^{''}+y^'+3y=2x-x^2

y^{^{''}} + y^{^{'}} + 3 y = 2 x - x^{2}