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Beliebt Rechnen >

(d^2y)/(dx^2)-9(dy)/(dx)+6y=xe^x

Lösung

\frac{d ^{2} y}{d x ^{2}} - 9 \frac{d y}{d x} + 6 y = x e^{x}

Lösung

y = c_{1} e^{\frac{( 9 + 57 ) x}{2}} + c_{2} e^{\frac{( 9 - 57 ) x}{2}} - \frac{e ^{x} x}{2} + \frac{7}{4} e^{x}

Schritte zur Lösung

\frac{d ^{2} y}{d x ^{2}} - 9 \frac{d y}{d x} + 6 y = x e^{x}

Solve linear ODE:

y = c_{1} e^{\frac{( 9 + 57 ) x}{2}} + c_{2} e^{\frac{( 9 - 57 ) x}{2}} - \frac{e ^{x} x}{2} + \frac{7}{4} e^{x}

y = c_{1} e^{\frac{( 9 + 57 ) x}{2}} + c_{2} e^{\frac{( 9 - 57 ) x}{2}} - \frac{e ^{x} x}{2} + \frac{7}{4} e^{x}

Graph

Beliebte Beispiele

(D^2-4D+4)y=e^{-4x}+5cos(3x)

(D^{2} - 4 D + 4) y = e^{- 4 x} + 5 cos (3 x)

(d^2y)/(dx^2)+6(dy)/(dx)+10y=50x

\frac{d ^{2} y}{d x ^{2}} + 6 \frac{d y}{d x} + 10 y = 50 x

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

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

y^{''}+8y^'+16y=4e^{-4t}

y^{^{''}} + 8 y^{^{'}} + 16 y = 4 e^{- 4 t}

y^{''}-3y^'+2y=3cos(3t),y(0)=2,y^'(0)=3

y^{^{''}} - 3 y^{^{'}} + 2 y = 3 cos (3 t), y (0) = 2, y^{^{'}} (0) = 3