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Beliebt Rechnen >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Solve linear ODE:

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

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

Graph

Beliebte Beispiele

derivative of arcsin(x/4)

\frac{d}{d x} (arcsin (\frac{x}{4}))

derivative of tan^4(3x)

\frac{d}{d x} (tan^{4} (3 x))

integral of y^3e^{-y}

\int y^{3} e^{- y} d y

(dy)/(dx)=e^{2x-1}y^2

\frac{d y}{d x} = e^{2 x - 1} y^{2}

integral of (sqrt(x^2+25))/(x^2)

\int \frac{x ^{2} + 25}{x ^{2}} d x