3y^{''}-5y^'+y=x^2+1+sin(2x)

解

3 y^{^{''}} - 5 y^{^{'}} + y = x^{2} + 1 + sin (2 x)

y = c_{1} e^{\frac{( 5 + 13 ) x}{6}} + c_{2} e^{\frac{( 5 - 13 ) x}{6}} + x^{2} + 10 x + 45 - \frac{11}{221} sin (2 x) + \frac{10}{221} cos (2 x)

解答ステップ

3 y^{''} (x) - 5 y^{'} (x) + y = x^{2} + 1 + sin (2 x)

線形 ODE を解く:

y = c_{1} e^{\frac{( 5 + 13 ) x}{6}} + c_{2} e^{\frac{( 5 - 13 ) x}{6}} + x^{2} + 10 x + 45 - \frac{11}{221} sin (2 x) + \frac{10}{221} cos (2 x)

y = c_{1} e^{\frac{( 5 + 13 ) x}{6}} + c_{2} e^{\frac{( 5 - 13 ) x}{6}} + x^{2} + 10 x + 45 - \frac{11}{221} sin (2 x) + \frac{10}{221} cos (2 x)