2y^{''}-7y^'+5y=-29

解答

2 y^{^{''}} - 7 y^{^{'}} + 5 y = - 29

y = c_{1} e^{\frac{5 t}{2}} + c_{2} e^{t} - \frac{29}{5}

求解步骤

2 y^{''} (t) - 7 y^{'} (t) + 5 y = - 29

求解线性方程:

y = c_{1} e^{\frac{5 t}{2}} + c_{2} e^{t} - \frac{29}{5}

y = c_{1} e^{\frac{5 t}{2}} + c_{2} e^{t} - \frac{29}{5}

y^{^{''}} + 8 y^{^{'}} + 16 y = e^{- 4 t}

y^{^{''}} + 9 y = sin (3 x) + e^{- x}

(D^{2} - 2 D + 1) y = x^{2} e^{3 x}

(d^{2} - 1) y = x sin (x) + (1 + x^{2}) e^{x}

3 x^{^{''}} - 30 x^{^{'}} + 75 x = 2 t + 1