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

Lösung

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

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

Schritte zur Lösung

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

Solve linear ODE:

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

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

y^{^{''}} + 2 y^{^{'}} + 2 y = 2 cos (x) + sin (x)

y^{^{''}} + 2 y^{^{'}} - 3 y = 32 (3 x + 1) e^{- 3 x}

y^{^{''}} + y^{^{'}} = cos (2 t), y (0) = 0, y^{^{'}} (0) = 1

y^{^{''}} - 2 y^{^{'}} + 1 = e^{x}

y^{^{''}} - 4 y = cos^{2} (x)