y^{''}-9y=(x^2-7)sin(3x)

解答

y^{^{''}} - 9 y = (x^{2} - 7) sin (3 x)

y = c_{1} e^{3 x} + c_{2} e^{- 3 x} - \frac{x ^{2} sin ( 3 x )}{18} - \frac{x cos ( 3 x )}{27} + \frac{32}{81} sin (3 x)

求解步骤

y^{''} (x) - 9 y = (x^{2} - 7) sin (3 x)

求解线性方程:

y = c_{1} e^{3 x} + c_{2} e^{- 3 x} - \frac{x ^{2} sin ( 3 x )}{18} - \frac{x cos ( 3 x )}{27} + \frac{32}{81} sin (3 x)

y = c_{1} e^{3 x} + c_{2} e^{- 3 x} - \frac{x ^{2} sin ( 3 x )}{18} - \frac{x cos ( 3 x )}{27} + \frac{32}{81} sin (3 x)

y^{^{''}} + 36 y = csc^{2} (6 x)

y^{^{''}} + 6 y^{^{'}} - 40 y = 1 - 3 x + x^{2}

y^{^{''}} + 10 y^{^{'}} + 25 y = e^{2 x}, y (0) = 0, y^{^{'}} (0) = 0

y^{^{''}} + 6 y^{^{'}} + 45 y = 6, y (0) = 5, y^{^{'}} (0) = 9

y^{^{''}} + 5 y^{^{'}} + 4 y = 3 e^{- 5 x}, y (0) = 5, y^{^{'}} (0) = 3