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Beliebt Rechnen >

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

Lösung

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

Lösung

y = c_{1} e^{2 x} + c_{2} e^{- 2 x} - \frac{x ^{2}}{4} - \frac{1}{8}

Schritte zur Lösung

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

Solve linear ODE:

y = c_{1} e^{2 x} + c_{2} e^{- 2 x} - \frac{x ^{2}}{4} - \frac{1}{8}

y = c_{1} e^{2 x} + c_{2} e^{- 2 x} - \frac{x ^{2}}{4} - \frac{1}{8}

Graph

Beliebte Beispiele

y^{'''}+y^{''}=12x^5

y^{^{'''}} + y^{^{''}} = 12 x^{5}

y^{''}-6y^'+9y=x^{-3}e^{3x}

y^{^{''}} - 6 y^{^{'}} + 9 y = x^{- 3} e^{3 x}

y^{''}+3y^'+2y=12x^2

y^{^{''}} + 3 y^{^{'}} + 2 y = 12 x^{2}

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

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

y^{''}-4y^'+5y=125t^2,y(0)=0,y^'(0)=0

y^{^{''}} - 4 y^{^{'}} + 5 y = 125 t^{2}, y (0) = 0, y^{^{'}} (0) = 0