y^{''}-3y^'-9y=4cos(2x)-5e^x

解答

y^{^{''}} - 3 y^{^{'}} - 9 y = 4 cos (2 x) - 5 e^{x}

y = c_{1} e^{\frac{( 3 + 3 5 ) x}{2}} + c_{2} e^{\frac{( 3 - 3 5 ) x}{2}} - \frac{24}{205} sin (2 x) - \frac{52}{205} cos (2 x) + \frac{5}{11} e^{x}

求解步骤

y^{''} (x) - 3 y^{'} (x) - 9 y = 4 cos (2 x) - 5 e^{x}

求解线性方程:

y = c_{1} e^{\frac{( 3 + 3 5 ) x}{2}} + c_{2} e^{\frac{( 3 - 3 5 ) x}{2}} - \frac{24}{205} sin (2 x) - \frac{52}{205} cos (2 x) + \frac{5}{11} e^{x}

y = c_{1} e^{\frac{( 3 + 3 5 ) x}{2}} + c_{2} e^{\frac{( 3 - 3 5 ) x}{2}} - \frac{24}{205} sin (2 x) - \frac{52}{205} cos (2 x) + \frac{5}{11} e^{x}

2 y^{^{''}} - 5 y^{^{'}} - 3 y = 1 + 2 e^{t} + e^{2 t}

x^{^{''}} + 100 x^{^{'}} + 2470 = 0

x^{^{''}} - 9 x^{^{'}} - 14 = 0

x^{^{''}} - 10 x^{^{'}} + 25 x = 78 t^{2} e^{5 t}

y^{^{''}} + 2 y^{^{'}} + y = 1, y (0) = 2, y^{^{'}} (0) = 1