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Beliebt Rechnen >

(d^2y)/(dx^2)-2(dy)/(dx)+y=x^{-2}e^x

Lösung

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

Lösung

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

Schritte zur Lösung

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

Solve linear ODE:

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

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

Graph

Beliebte Beispiele

x^{''}+2x^'+5x=sin(2t)

x^{^{''}} + 2 x^{^{'}} + 5 x = sin (2 t)

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

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

y^{''}+3y^'+2y=12e^t

y^{^{''}} + 3 y^{^{'}} + 2 y = 12 e^{t}

y^{''}-2y^'-3y=3t^2

y^{^{''}} - 2 y^{^{'}} - 3 y = 3 t^{2}

(D^2-2D+3)y=x^3+sin(x)

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