y^{''}+2y^'-35y=13sin(x)-e^{3x}+1

解答

y^{^{''}} + 2 y^{^{'}} - 35 y = 13 sin (x) - e^{3 x} + 1

y = c_{1} e^{5 x} + c_{2} e^{- 7 x} - \frac{9}{25} sin (x) - \frac{1}{50} cos (x) + \frac{1}{20} e^{3 x} - \frac{1}{35}

求解步骤

y^{''} (x) + 2 y^{'} (x) - 35 y = 13 sin (x) - e^{3 x} + 1

求解线性方程:

y = c_{1} e^{5 x} + c_{2} e^{- 7 x} - \frac{9}{25} sin (x) - \frac{1}{50} cos (x) + \frac{1}{20} e^{3 x} - \frac{1}{35}

y = c_{1} e^{5 x} + c_{2} e^{- 7 x} - \frac{9}{25} sin (x) - \frac{1}{50} cos (x) + \frac{1}{20} e^{3 x} - \frac{1}{35}

y^{^{''}} + a y^{^{'}} + y = e^{- 4 t}

y^{^{''}} + 9 y = 6 cos (3 x)

(D^{2} - 3 D + 2) y = e^{3 x}

\frac{5}{6} q^{^{''}} + 10 q^{^{'}} + 60 q = 600

x^{^{''}} + \frac{1.0889}{19.6} x = cos (2 t)