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

解

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

y = e^{\frac{x}{2}} (c_{1} cos (\frac{15 x}{2}) + c_{2} sin (\frac{15 x}{2})) + cos (2 x)

解答ステップ

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

線形 ODE を解く:

y = e^{\frac{x}{2}} (c_{1} cos (\frac{15 x}{2}) + c_{2} sin (\frac{15 x}{2})) + cos (2 x)

y = e^{\frac{x}{2}} (c_{1} cos (\frac{15 x}{2}) + c_{2} sin (\frac{15 x}{2})) + cos (2 x)