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Beliebt Rechnen >

y^{''}-15y^'+54y=e^{ax}

Lösung

y^{^{''}} - 15 y^{^{'}} + 54 y = e^{a x}

Lösung

y = c_{1} e^{9 x} + c_{2} e^{6 x} + \frac{e ^{a x}}{a ^{2} - 15 a + 54}

Schritte zur Lösung

y^{''} (x) - 15 y^{'} (x) + 54 y = e^{a x}

Solve linear ODE:

y = c_{1} e^{9 x} + c_{2} e^{6 x} + \frac{e ^{a x}}{a ^{2} - 15 a + 54}

y = c_{1} e^{9 x} + c_{2} e^{6 x} + \frac{e ^{a x}}{a ^{2} - 15 a + 54}

Graph

Beliebte Beispiele

y^{'''}+9y^{''}+y^'+9y=16e^x-9

y^{^{'''}} + 9 y^{^{''}} + y^{^{'}} + 9 y = 16 e^{x} - 9

y^{''}+8y^'+32y=2e^{2x}

y^{^{''}} + 8 y^{^{'}} + 32 y = 2 e^{2 x}

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

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

y^{''}-6y^'+9y=4e^3tln(t)

y^{^{''}} - 6 y^{^{'}} + 9 y = 4 e^{3} t ln (t)

y^{''}+y=cos(2t)cos(t)

y^{^{''}} + y = cos (2 t) cos (t)