y^{''}+7y^'+14y=1096e^{2t}cos(8t)

解答

y^{^{''}} + 7 y^{^{'}} + 14 y = 1096 e^{2 t} cos (8 t)

y = e^{- \frac{7 t}{2}} (c_{1} cos (\frac{7 t}{2}) + c_{2} sin (\frac{7 t}{2})) + 11 e^{2 t} sin (8 t) - 4 e^{2 t} cos (8 t)

求解步骤

y^{''} (t) + 7 y^{'} (t) + 14 y = 1096 e^{2 t} cos (8 t)

求解线性方程:

y = e^{- \frac{7 t}{2}} (c_{1} cos (\frac{7 t}{2}) + c_{2} sin (\frac{7 t}{2})) + 11 e^{2 t} sin (8 t) - 4 e^{2 t} cos (8 t)

y = e^{- \frac{7 t}{2}} (c_{1} cos (\frac{7 t}{2}) + c_{2} sin (\frac{7 t}{2})) + 11 e^{2 t} sin (8 t) - 4 e^{2 t} cos (8 t)

x \to 4 - lim (\frac{x}{x ^{2} - 16})

\frac{d y}{d x} = \frac{x}{25 y}, y (5) = 1

l a pl a ce t r an s f or m cos (t) \cdot e^{t}

\int \frac{tan ^{3} ( x )}{sec ^{2} ( x ) - 1} d x

d er i v a t i v e y = ln (x ln (x))