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Beliebt Rechnen >

y^{''}-y^'-12y=e^{2x}+e^x-2

Lösung

y^{^{''}} - y^{^{'}} - 12 y = e^{2 x} + e^{x} - 2

Lösung

y = c_{1} e^{4 x} + c_{2} e^{- 3 x} - \frac{1}{10} e^{2 x} - \frac{1}{12} e^{x} + \frac{1}{6}

Schritte zur Lösung

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

Solve linear ODE:

y = c_{1} e^{4 x} + c_{2} e^{- 3 x} - \frac{1}{10} e^{2 x} - \frac{1}{12} e^{x} + \frac{1}{6}

y = c_{1} e^{4 x} + c_{2} e^{- 3 x} - \frac{1}{10} e^{2 x} - \frac{1}{12} e^{x} + \frac{1}{6}

Graph

Beliebte Beispiele

y^{'''}+64y^'=sec(8x)

y^{^{'''}} + 64 y^{^{'}} = sec (8 x)

y^{''}+y^'-2y=4x^2

y^{^{''}} + y^{^{'}} - 2 y = 4 x^{2}

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

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

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

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

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

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