(d^3-3d^2-10d+24)y=2x^2+5

Lösung

(d^{3} - 3 d^{2} - 10 d + 24) y = 2 x^{2} + 5

y = c_{1} e^{2 x} + c_{2} e^{- 3 x} + c_{3} e^{4 x} + \frac{x ^{2}}{12} + \frac{5 x}{72} + \frac{223}{864}

Schritte zur Lösung

(d^{3} - 3 d^{2} - 10 d + 24) y = 2 x^{2} + 5

Solve linear ODE:

y = c_{1} e^{2 x} + c_{2} e^{- 3 x} + c_{3} e^{4 x} + \frac{x ^{2}}{12} + \frac{5 x}{72} + \frac{223}{864}

y = c_{1} e^{2 x} + c_{2} e^{- 3 x} + c_{3} e^{4 x} + \frac{x ^{2}}{12} + \frac{5 x}{72} + \frac{223}{864}

l in e a r y^{^{''}} - y^{^{'}} + 2 = 0

y^{^{'''}} - y^{^{'}} = x e^{(- x)} + 5 cos (x)

y^{^{'''}} - y = 1, y (0) = 0, y^{^{'}} (0) = 0, y^{^{''}} (0) = 0

y^{^{''}} + y^{^{'}} - 12 y = 12

y^{^{'''}} - 3 y^{^{''}} + 3 y^{^{'}} - y = x - 8 e x