y^{'''}-y^{''}+9y^'-145y=0,y(0)=e^{5x}

Lösung

y^{^{'''}} - y^{^{''}} + 9 y^{^{'}} - 145 y = 0, y (0) = e^{5 x}

y = c_{1} e^{5 x} + e^{- 2 x} (c_{2} cos (5 x) + c_{3} sin (5 x))

Schritte zur Lösung

y^{'''} (x) - y^{''} (x) + 9 y^{'} (x) - 145 y = 0

Solve linear ODE:

y = c_{1} e^{5 x} + e^{- 2 x} (c_{2} cos (5 x) + c_{3} sin (5 x))

y = c_{1} e^{5 x} + e^{- 2 x} (c_{2} cos (5 x) + c_{3} sin (5 x))