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Beliebt Rechnen >

y^{''}-4y^'+4y=(x+1)e^2x

Lösung

y^{^{''}} - 4 y^{^{'}} + 4 y = (x + 1) e^{2} x

Lösung

y = c_{1} e^{2 x} + c_{2} x e^{2 x} + \frac{e ^{2} x ^{2}}{4} + \frac{3 e ^{2} x}{4} + \frac{5 e ^{2}}{8}

Schritte zur Lösung

y^{''} (x) - 4 y^{'} (x) + 4 y = (x + 1) e^{2} x

Solve linear ODE:

y = c_{1} e^{2 x} + c_{2} x e^{2 x} + \frac{e ^{2} x ^{2}}{4} + \frac{3 e ^{2} x}{4} + \frac{5 e ^{2}}{8}

y = c_{1} e^{2 x} + c_{2} x e^{2 x} + \frac{e ^{2} x ^{2}}{4} + \frac{3 e ^{2} x}{4} + \frac{5 e ^{2}}{8}

Graph

Beliebte Beispiele

(d^2-4d-12)*y=(x-1)*e^{-2x}

(d^{2} - 4 d - 12) \cdot y = (x - 1) \cdot e^{- 2 x}

(d^2+4d+4)y=x^2+e^x+cos(x)

(d^{2} + 4 d + 4) y = x^{2} + e^{x} + cos (x)

(d^2-3d+2)y=5e^3x

(d^{2} - 3 d + 2) y = 5 e^{3} x

(d^2-4d+4)y=8x^2e^2x

(d^{2} - 4 d + 4) y = 8 x^{2} e^{2} x

(d^2-2d-3)*y=x^3*e^{-3x}

(d^{2} - 2 d - 3) \cdot y = x^{3} \cdot e^{- 3 x}