3xy^{''}-2xy^'+11xy=0

解答

3 x y^{^{''}} - 2 x y^{^{'}} + 11 x y = 0

y = e^{\frac{x}{3}} (c_{1} cos (\frac{4 2 x}{3}) + c_{2} sin (\frac{4 2 x}{3}))

求解步骤

3 x y^{''} (x) - 2 x y^{'} (x) + 11 x y = 0

求解线性方程:

y = e^{\frac{x}{3}} (c_{1} cos (\frac{4 2 x}{3}) + c_{2} sin (\frac{4 2 x}{3}))

y = e^{\frac{x}{3}} (c_{1} cos (\frac{4 2 x}{3}) + c_{2} sin (\frac{4 2 x}{3}))

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

y^{^{''}} - 6 y^{^{'}} + 9 y = 0, y = e^{3 x}

y^{^{'''}} - y^{^{''}} + 100 y^{^{'}} - 100 y = 0

y^{^{''}} + 9 y^{^{'}} + 14 y = 0, y (0) = 0

x^{^{''}} + 2 ab x^{^{'}} + b^{2} x = 0