y^{''}-y^'+y=25sin(2x)

解

y^{^{''}} - y^{^{'}} + y = 25 sin (2 x)

y = e^{\frac{x}{2}} (c_{1} cos (\frac{3 x}{2}) + c_{2} sin (\frac{3 x}{2})) - \frac{75}{13} sin (2 x) + \frac{50}{13} cos (2 x)

解答ステップ

y^{''} (x) - y^{'} (x) + y = 25 sin (2 x)

線形 ODE を解く:

y = e^{\frac{x}{2}} (c_{1} cos (\frac{3 x}{2}) + c_{2} sin (\frac{3 x}{2})) - \frac{75}{13} sin (2 x) + \frac{50}{13} cos (2 x)

y = e^{\frac{x}{2}} (c_{1} cos (\frac{3 x}{2}) + c_{2} sin (\frac{3 x}{2})) - \frac{75}{13} sin (2 x) + \frac{50}{13} cos (2 x)