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Beliebt Rechnen >

(d^2y)/(dx^2)-9(dy)/(dx)+5y=xe^x

Lösung

\frac{d ^{2} y}{d x ^{2}} - 9 \frac{d y}{d x} + 5 y = x e^{x}

Lösung

y = c_{1} e^{\frac{( 9 + 61 ) x}{2}} + c_{2} e^{\frac{( 9 - 61 ) x}{2}} - \frac{e ^{x} x}{3} + \frac{7}{9} e^{x}

Schritte zur Lösung

\frac{d ^{2} y}{d x ^{2}} - 9 \frac{d y}{d x} + 5 y = x e^{x}

Solve linear ODE:

y = c_{1} e^{\frac{( 9 + 61 ) x}{2}} + c_{2} e^{\frac{( 9 - 61 ) x}{2}} - \frac{e ^{x} x}{3} + \frac{7}{9} e^{x}

y = c_{1} e^{\frac{( 9 + 61 ) x}{2}} + c_{2} e^{\frac{( 9 - 61 ) x}{2}} - \frac{e ^{x} x}{3} + \frac{7}{9} e^{x}

Graph

Beliebte Beispiele

y^{''}+4y^'+4y=e^{-t},y(0)=0,y^'(0)=1

y^{^{''}} + 4 y^{^{'}} + 4 y = e^{- t}, y (0) = 0, y^{^{'}} (0) = 1

y^{''}-2y^'-3y=3t^2+4t-5

y^{^{''}} - 2 y^{^{'}} - 3 y = 3 t^{2} + 4 t - 5

y^{''}-y=7.1cos(t),y(0)=0,y^'(0)=7.1

y^{^{''}} - y = 7.1 cos (t), y (0) = 0, y^{^{'}} (0) = 7.1

y^{''}-4y^'+3y=8e^x

y^{^{''}} - 4 y^{^{'}} + 3 y = 8 e^{x}

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

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