y^{'''}-6y^{''}=4-sin(x)

解

y^{^{'''}} - 6 y^{^{''}} = 4 - sin (x)

y = c_{1} e^{6 x} + c_{2} + c_{3} x - \frac{x ^{2}}{3} - \frac{6}{37} sin (x) - \frac{1}{37} cos (x)

解答ステップ

y^{'''} (x) - 6 y^{''} (x) = 4 - sin (x)

線形 ODE を解く:

y = c_{1} e^{6 x} + c_{2} + c_{3} x - \frac{x ^{2}}{3} - \frac{6}{37} sin (x) - \frac{1}{37} cos (x)

y = c_{1} e^{6 x} + c_{2} + c_{3} x - \frac{x ^{2}}{3} - \frac{6}{37} sin (x) - \frac{1}{37} cos (x)