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Beliebt Rechnen >

y^{''}+4y^'+4y=4x^2+6e^x

Lösung

y^{^{''}} + 4 y^{^{'}} + 4 y = 4 x^{2} + 6 e^{x}

Lösung

y = c_{1} e^{- 2 x} + c_{2} x e^{- 2 x} + x^{2} - 2 x + \frac{3}{2} + \frac{2}{3} e^{x}

Schritte zur Lösung

y^{''} (x) + 4 y^{'} (x) + 4 y = 4 x^{2} + 6 e^{x}

Solve linear ODE:

y = c_{1} e^{- 2 x} + c_{2} x e^{- 2 x} + x^{2} - 2 x + \frac{3}{2} + \frac{2}{3} e^{x}

y = c_{1} e^{- 2 x} + c_{2} x e^{- 2 x} + x^{2} - 2 x + \frac{3}{2} + \frac{2}{3} e^{x}

Graph

Beliebte Beispiele

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

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

9y^{''}+4y=3x+12e^{-x},y(0)=1,y^'(0)=0

9 y^{^{''}} + 4 y = 3 x + 12 e^{- x}, y (0) = 1, y^{^{'}} (0) = 0

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

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

4y^{''}-3y^'=4x-6

4 y^{^{''}} - 3 y^{^{'}} = 4 x - 6

y^{''}-9y^'+8y=x,y(0)=e^x

y^{^{''}} - 9 y^{^{'}} + 8 y = x, y (0) = e^{x}