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Beliebt Rechnen >

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

Lösung

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

Lösung

y = c_{1} e^{- 2 x} + c_{2} x e^{- 2 x} + \frac{x ^{2}}{4} - \frac{x}{2} + \frac{3}{8}

Schritte zur Lösung

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

Solve linear ODE:

y = c_{1} e^{- 2 x} + c_{2} x e^{- 2 x} + \frac{x ^{2}}{4} - \frac{x}{2} + \frac{3}{8}

y = c_{1} e^{- 2 x} + c_{2} x e^{- 2 x} + \frac{x ^{2}}{4} - \frac{x}{2} + \frac{3}{8}

Graph

Beliebte Beispiele

integral of (8x^5-5x^4-4x^3-6x^2-2x-3)

\int (8 x^{5} - 5 x^{4} - 4 x^{3} - 6 x^{2} - 2 x - 3) d x

derivative (30000)/(1.8t+9)

d er i v a t i v e \frac{30000}{1.8 t + 9}

integral of 1/(4-3x)

\int \frac{1}{4 - 3 x} d x

steigung (2.5)(-1.7)

s l o p e (2.5) (- 1.7)

limit as x approaches 0 of (x^4)/(x^2)

x \to 0 lim (\frac{x ^{4}}{x ^{2}})