y^{''}+14y^'+28y=6675e^{2t}cos(15t)

解答

y^{^{''}} + 14 y^{^{'}} + 28 y = 6675 e^{2 t} cos (15 t)

y = c_{1} e^{(- 7 + 21) t} + c_{2} e^{(- 7 - 21) t} + 18 e^{2 t} sin (15 t) - 11 e^{2 t} cos (15 t)

求解步骤

y^{''} (t) + 14 y^{'} (t) + 28 y = 6675 e^{2 t} cos (15 t)

求解线性方程:

y = c_{1} e^{(- 7 + 21) t} + c_{2} e^{(- 7 - 21) t} + 18 e^{2 t} sin (15 t) - 11 e^{2 t} cos (15 t)

y = c_{1} e^{(- 7 + 21) t} + c_{2} e^{(- 7 - 21) t} + 18 e^{2 t} sin (15 t) - 11 e^{2 t} cos (15 t)

l a pl a ce t r an s f or m t^{2} sin (t)

d er i v a t i v e \frac{1 + 5 t}{ln ( t ^{2} )}

\int \frac{x ^{2}}{x ^{6} - 1} d x

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