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Beliebt Rechnen >

y^{''}-4y=8x^2

Lösung

y^{^{''}} - 4 y = 8 x^{2}

Lösung

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

Schritte zur Lösung

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

Solve linear ODE:

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

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

Graph

Beliebte Beispiele

x^{''}-4x^'+3x=(e^t)/(1+e^t)

x^{^{''}} - 4 x^{^{'}} + 3 x = \frac{e ^{t}}{1 + e ^{t}}

y^{''}-9y^'+18y=9+18x

y^{^{''}} - 9 y^{^{'}} + 18 y = 9 + 18 x

y^{''}+2y^'-3y=8e^{-3x}

y^{^{''}} + 2 y^{^{'}} - 3 y = 8 e^{- 3 x}

y^{''}+6y^'+9y=3

y^{^{''}} + 6 y^{^{'}} + 9 y = 3

y^{''}-16y=32+45e^x,y(0)=0,y^'(0)=1

y^{^{''}} - 16 y = 32 + 45 e^{x}, y (0) = 0, y^{^{'}} (0) = 1