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Beliebt Rechnen >

y^{''}-y^'-6y=-e^x+12x

Lösung

y^{^{''}} - y^{^{'}} - 6 y = - e^{x} + 12 x

Lösung

y = c_{1} e^{3 x} + c_{2} e^{- 2 x} + \frac{1}{6} e^{x} - 2 x + \frac{1}{3}

Schritte zur Lösung

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

Solve linear ODE:

y = c_{1} e^{3 x} + c_{2} e^{- 2 x} + \frac{1}{6} e^{x} - 2 x + \frac{1}{3}

y = c_{1} e^{3 x} + c_{2} e^{- 2 x} + \frac{1}{6} e^{x} - 2 x + \frac{1}{3}

Graph

Beliebte Beispiele

y^{''}-9y=sinh(3x)

y^{^{''}} - 9 y = sinh (3 x)

y^{''''}-2y^{'''}+y^{''}=e^x+1

y^{^{''''}} - 2 y^{^{'''}} + y^{^{''}} = e^{x} + 1

y^{''}+6y^'-7y=3e^{2x}-e^{-x}

y^{^{''}} + 6 y^{^{'}} - 7 y = 3 e^{2 x} - e^{- x}

(d^2y)/(dx^2)+(dy)/(dx)=tan(x)

\frac{d ^{2} y}{d x ^{2}} + \frac{d y}{d x} = tan (x)

y^{''}-2y^'-3y=12e^x-6

y^{^{''}} - 2 y^{^{'}} - 3 y = 12 e^{x} - 6