(10d^3+d^2-7d+2)y=0

Lösung

(10 d^{3} + d^{2} - 7 d + 2) y = 0

y = c_{1} e^{- x} + c_{2} e^{\frac{2 x}{5}} + c_{3} e^{\frac{x}{2}}

Schritte zur Lösung

(10 d^{3} + d^{2} - 7 d + 2) y = 0

Solve linear ODE:

y = c_{1} e^{- x} + c_{2} e^{\frac{2 x}{5}} + c_{3} e^{\frac{x}{2}}

y = c_{1} e^{- x} + c_{2} e^{\frac{2 x}{5}} + c_{3} e^{\frac{x}{2}}

l in e a r y^{^{'''}} + 3 y^{^{''}} - 8 y^{^{'}} - 30 y = 0

y^{^{'''}} - 7 y^{^{''}} - 8 y^{^{'}} + 16 y = 0

y^{^{''}} + y + y^{^{'}} = 0

y^{^{''}} - 12 y^{^{'}} + 36 y = 0, y (0) = 3, y^{^{'}} (0) = \frac{39}{2}

y^{^{''}} + 18 y^{^{'}} + 80 y = 0, y (0) = 9, y^{^{'}} (0) = - 76