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

解答

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

y = c_{1} e^{3 x} + c_{2} e^{- 3 x} - \frac{3}{122} e^{2 x} sin (5 x) - \frac{5}{244} e^{2 x} cos (5 x)

求解步骤

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

求解线性方程:

y = c_{1} e^{3 x} + c_{2} e^{- 3 x} - \frac{3}{122} e^{2 x} sin (5 x) - \frac{5}{244} e^{2 x} cos (5 x)

y = c_{1} e^{3 x} + c_{2} e^{- 3 x} - \frac{3}{122} e^{2 x} sin (5 x) - \frac{5}{244} e^{2 x} cos (5 x)

y^{^{''}} + 2 y^{^{'}} + 10 y = 17 sin (x) - 37 sin (3 x)

y^{^{''}} + 5 y + 6 y = 10 sin (x), y (0) = 1, y^{^{'}} (0) = - 4

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

y^{^{''}} + 8 y = 2 t^{4}, y (0) = 0, y^{^{'}} (0) = 0

y^{^{''}} - 4 y^{^{'}} + 4 y = x^{- 1} e^{2 x}