y^{''}-5y^'=2x^3-4x^2-x+6

Lösung

y^{^{''}} - 5 y^{^{'}} = 2 x^{3} - 4 x^{2} - x + 6

y = c_{1} e^{5 x} + c_{2} - \frac{x ^{4}}{10} + \frac{14 x ^{3}}{75} + \frac{53 x ^{2}}{250} - \frac{697 x}{625}

Schritte zur Lösung

y^{''} (x) - 5 y^{'} (x) = 2 x^{3} - 4 x^{2} - x + 6

Solve linear ODE:

y = c_{1} e^{5 x} + c_{2} - \frac{x ^{4}}{10} + \frac{14 x ^{3}}{75} + \frac{53 x ^{2}}{250} - \frac{697 x}{625}

y = c_{1} e^{5 x} + c_{2} - \frac{x ^{4}}{10} + \frac{14 x ^{3}}{75} + \frac{53 x ^{2}}{250} - \frac{697 x}{625}

(D^{2} + 4 D + 5) y = 50 x + 13 e^{3 x}

y^{^{''}} + y = 4 x cos (x)

y^{^{''}} + 4 y^{^{'}} + 3 y = 6 x^{2} + x + 9

y^{^{''}} - 3 y^{^{'}} + 2 y = e^{- 4 t}, y (0) = 1, y^{^{'}} (0) = 5

y^{^{''}} + 8 y^{^{'}} = 8 x