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Beliebt Rechnen >

2y^{''}-4y^'+2y=e^xx^{-1}

Lösung

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

Lösung

y = c_{1} e^{x} + c_{2} x e^{x} + \frac{- e ^{x} x + e ^{x} x ln ( x )}{2}

Schritte zur Lösung

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

Solve linear ODE:

y = c_{1} e^{x} + c_{2} x e^{x} + \frac{- e ^{x} x + e ^{x} x ln ( x )}{2}

y = c_{1} e^{x} + c_{2} x e^{x} + \frac{- e ^{x} x + e ^{x} x ln ( x )}{2}

Graph

Beliebte Beispiele

(d^2y)/(dx^2)-5(dy)/(dx)+6y=x^2

\frac{d ^{2} y}{d x ^{2}} - 5 \frac{d y}{d x} + 6 y = x^{2}

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

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

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

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

y^{''}+7y^'-12=e^{3x}-2e^x-5x

y^{^{''}} + 7 y^{^{'}} - 12 = e^{3 x} - 2 e^{x} - 5 x

y^{''}+2y^'+2y=1+cos(sqrt(2)t)

y^{^{''}} + 2 y^{^{'}} + 2 y = 1 + cos (2 t)