(d^2y)/(dx^2)-6(dy)/(dx)+9y=2sin(4x)

解答

\frac{d ^{2} y}{d x ^{2}} - 6 \frac{d y}{d x} + 9 y = 2 sin (4 x)

y = c_{1} e^{3 x} + c_{2} x e^{3 x} - \frac{14}{625} sin (4 x) + \frac{48}{625} cos (4 x)

求解步骤

\frac{d ^{2} y}{d x ^{2}} - 6 \frac{d y}{d x} + 9 y = 2 sin (4 x)

求解线性方程:

y = c_{1} e^{3 x} + c_{2} x e^{3 x} - \frac{14}{625} sin (4 x) + \frac{48}{625} cos (4 x)

y = c_{1} e^{3 x} + c_{2} x e^{3 x} - \frac{14}{625} sin (4 x) + \frac{48}{625} cos (4 x)

y^{^{''}} + 5 y = 6 t^{2} - 9, y (0) = 0, y^{^{'}} (0) = - 3

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

y^{^{''}} - 3 y^{^{'}} + 2 y = 5 x e^{2 x} + 10 sin (2 x)

x^{^{''}} - 2 x^{^{'}} + x = 3 t e^{- t}

y^{^{''}} + (- 8) y^{^{'}} + 20 y = 100 x^{2} - 65 x e^{x}