(d^2y)/(dx^2)-(dy)/(dx)+y=2sin(3x)

解

\frac{d ^{2} y}{d x ^{2}} - \frac{d y}{d x} + y = 2 sin (3 x)

y = e^{\frac{x}{2}} (c_{1} cos (\frac{3 x}{2}) + c_{2} sin (\frac{3 x}{2})) - \frac{16}{73} sin (3 x) + \frac{6}{73} cos (3 x)

解答ステップ

\frac{d ^{2} y}{d x ^{2}} - \frac{d y}{d x} + y = 2 sin (3 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{16}{73} sin (3 x) + \frac{6}{73} cos (3 x)

y = e^{\frac{x}{2}} (c_{1} cos (\frac{3 x}{2}) + c_{2} sin (\frac{3 x}{2})) - \frac{16}{73} sin (3 x) + \frac{6}{73} cos (3 x)