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Beliebt Rechnen >

(d^2y)/(dx^2)-4y^'-12y=2x+6

Lösung

\frac{d ^{2} y}{d x ^{2}} - 4 y^{^{'}} - 12 y = 2 x + 6

Lösung

y = c_{1} e^{6 x} + c_{2} e^{- 2 x} - \frac{x}{6} - \frac{4}{9}

Schritte zur Lösung

y^{''} (x) - 4 y^{'} (x) - 12 y = 2 x + 6

Solve linear ODE:

y = c_{1} e^{6 x} + c_{2} e^{- 2 x} - \frac{x}{6} - \frac{4}{9}

y = c_{1} e^{6 x} + c_{2} e^{- 2 x} - \frac{x}{6} - \frac{4}{9}

Graph

Beliebte Beispiele

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

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

y^{''}+20y^'+200y=1

y^{^{''}} + 20 y^{^{'}} + 200 y = 1

y^{''}+20y^'+200y=2

y^{^{''}} + 20 y^{^{'}} + 200 y = 2

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

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

y^{''}+y=e^x+x^3,y(0)=2,y^'(0)=0

y^{^{''}} + y = e^{x} + x^{3}, y (0) = 2, y^{^{'}} (0) = 0