1/6 y^{''}+6y=tan(6t)-1/2 e^{2t}

解

\frac{1}{6} y^{^{''}} + 6 y = tan (6 t) - \frac{1}{2} e^{2 t}

y = c_{1} cos (6 t) + c_{2} sin (6 t) + \frac{- 20 cos ( 6 t ) ln ( tan ( 6 t ) + sec ( 6 t ) ) - 9 e ^{2 t} cos ^{2} ( 6 t ) - 9 e ^{2 t} sin ^{2} ( 6 t )}{120}

解答ステップ

\frac{1}{6} y^{''} (t) + 6 y = tan (6 t) - \frac{1}{2} e^{2 t}

線形 ODE を解く:

y = c_{1} cos (6 t) + c_{2} sin (6 t) + \frac{- 20 cos ( 6 t ) ln ( tan ( 6 t ) + sec ( 6 t ) ) - 9 e ^{2 t} cos ^{2} ( 6 t ) - 9 e ^{2 t} sin ^{2} ( 6 t )}{120}

y = c_{1} cos (6 t) + c_{2} sin (6 t) + \frac{- 20 cos ( 6 t ) ln ( tan ( 6 t ) + sec ( 6 t ) ) - 9 e ^{2 t} cos ^{2} ( 6 t ) - 9 e ^{2 t} sin ^{2} ( 6 t )}{120}