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Beliebt Rechnen >

y^{''}+3y^'+2y=x^2-1

Lösung

y^{^{''}} + 3 y^{^{'}} + 2 y = x^{2} - 1

Lösung

y = c_{1} e^{- x} + c_{2} e^{- 2 x} + \frac{x ^{2}}{2} - \frac{3 x}{2} + \frac{5}{4}

Schritte zur Lösung

y^{''} (x) + 3 y^{'} (x) + 2 y = x^{2} - 1

Solve linear ODE:

y = c_{1} e^{- x} + c_{2} e^{- 2 x} + \frac{x ^{2}}{2} - \frac{3 x}{2} + \frac{5}{4}

y = c_{1} e^{- x} + c_{2} e^{- 2 x} + \frac{x ^{2}}{2} - \frac{3 x}{2} + \frac{5}{4}

Graph

Beliebte Beispiele

y^{''}-3y^'-4y=3e^2x

y^{^{''}} - 3 y^{^{'}} - 4 y = 3 e^{2} x

y^{''}-4y^'+5y=(2e^{2x})/(sin(x))

y^{^{''}} - 4 y^{^{'}} + 5 y = \frac{2 e ^{2 x}}{sin ( x )}

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

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

y^{''}+9y=xe^{3x}

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

(D^2-3D+2)y=72xe^{-x}

(D^{2} - 3 D + 2) y = 72 x e^{- x}