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

Lösung

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

y = c_{1} e^{x} + c_{2} e^{- 2 x} + c_{3} e^{3 x} + \frac{- e ^{x} x + x ^{2}}{6} + \frac{5 x}{18} + \frac{37}{108}

Schritte zur Lösung

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

Solve linear ODE:

y = c_{1} e^{x} + c_{2} e^{- 2 x} + c_{3} e^{3 x} + \frac{- e ^{x} x + x ^{2}}{6} + \frac{5 x}{18} + \frac{37}{108}

y = c_{1} e^{x} + c_{2} e^{- 2 x} + c_{3} e^{3 x} + \frac{- e ^{x} x + x ^{2}}{6} + \frac{5 x}{18} + \frac{37}{108}

x^{^{''}} + 3 x^{^{'}} + 2 x = sin (3 t)

x^{^{''}} + 8 x^{^{'}} + 16 = 0

x^{^{''''}} - x^{^{''}} = 1

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

y^{^{''}} - 4 y^{^{'}} - 5 y = 125