y^{''}-5y^'-6y=xe-5x

Lösung

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

y = c_{1} e^{6 x} + c_{2} e^{- x} + \frac{( - e + 5 ) x}{6} - \frac{5 ( - e + 5 )}{36}

Schritte zur Lösung

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

Solve linear ODE:

y = c_{1} e^{6 x} + c_{2} e^{- x} + \frac{( - e + 5 ) x}{6} - \frac{5 ( - e + 5 )}{36}

y = c_{1} e^{6 x} + c_{2} e^{- x} + \frac{( - e + 5 ) x}{6} - \frac{5 ( - e + 5 )}{36}

\frac{1}{8} y^{^{''}} + 8 x + 4 y^{^{'}} = 0, y^{^{'}} (0) = 9, y (0) = 0

\frac{d ^{2} y}{d x ^{2}} + 2 \frac{d y}{d x} + 1 = 0

y^{^{''}} - 16 y = cos (4 t), y (0) = 0, y^{^{'}} (0) = 2

y^{^{''}} - 9 y^{^{'}} + 20 = 0

y^{^{''}} + 5 y^{^{'}} + 6 y = \frac{1}{x}, y (0) = 0, y^{^{'}} (0) = 1