7y^{''}+5y^'-y=9

解答

7 y^{^{''}} + 5 y^{^{'}} - y = 9

y = c_{1} e^{\frac{( - 5 + 53 ) t}{14}} + c_{2} e^{\frac{( - 5 - 53 ) t}{14}} - 9

求解步骤

7 y^{''} (t) + 5 y^{'} (t) - y = 9

求解线性方程:

y = c_{1} e^{\frac{( - 5 + 53 ) t}{14}} + c_{2} e^{\frac{( - 5 - 53 ) t}{14}} - 9

y = c_{1} e^{\frac{( - 5 + 53 ) t}{14}} + c_{2} e^{\frac{( - 5 - 53 ) t}{14}} - 9

y^{^{''}} + 3 y^{^{'}} + 2.25 y = 9 t^{3} + 64, y (0) = 1, y^{^{'}} (0) = 31.5

y^{^{''}} + 3 y^{^{'}} - 4 y = - 32 t^{2}

y^{^{''}} + y^{^{'}} = (2 t)

y^{^{''}} + 3 y + 2 = 0, y (2) = - 1, y^{^{'}} (0) = 0

y^{^{''}} - 2 y^{^{'}} + 2 y = e - t, y (0) = 0, y^{^{'}} (0) = 1