y^{''}-5y^'+6y=pix^2+3

解答

y^{^{''}} - 5 y^{^{'}} + 6 y = π x^{2} + 3

y = c_{1} e^{3 x} + c_{2} e^{2 x} + \frac{π x ^{2}}{6} + \frac{5 π x}{18} + \frac{54 + 19 π}{108}

求解步骤

y^{''} (x) - 5 y^{'} (x) + 6 y = π x^{2} + 3

求解线性方程:

y = c_{1} e^{3 x} + c_{2} e^{2 x} + \frac{π x ^{2}}{6} + \frac{5 π x}{18} + \frac{54 + 19 π}{108}

y = c_{1} e^{3 x} + c_{2} e^{2 x} + \frac{π x ^{2}}{6} + \frac{5 π x}{18} + \frac{54 + 19 π}{108}

y^{^{'''}} + y^{^{''}} = 9 x^{2}

y^{^{''}} - 9 y^{^{'}} + 4 y = x e^{x}

y^{^{''}} + 4 y = sec^{2} (x)

y^{^{''}} + 2 y^{^{'}} - 3 y = 1, y (0) = e^{x} - \frac{1}{3}

y^{^{'''}} - 12 y^{^{''}} + 256 y = e^{8 x}