1/6 y^{''}+6y=3tan(6t)-1/3 e^{4t}

解

\frac{1}{6} y^{^{''}} + 6 y = 3 tan (6 t) - \frac{1}{3} e^{4 t}

y = c_{1} cos (6 t) + c_{2} sin (6 t) - \frac{e ^{4 t} cos ^{2} ( 6 t ) + e ^{4 t} sin ^{2} ( 6 t ) + 13 cos ( 6 t ) ln ( sec ( 6 t ) + tan ( 6 t ) )}{26}

解答ステップ

\frac{1}{6} y^{''} (t) + 6 y = 3 tan (6 t) - \frac{1}{3} e^{4 t}

線形 ODE を解く:

y = c_{1} cos (6 t) + c_{2} sin (6 t) - \frac{e ^{4 t} cos ^{2} ( 6 t ) + e ^{4 t} sin ^{2} ( 6 t ) + 13 cos ( 6 t ) ln ( sec ( 6 t ) + tan ( 6 t ) )}{26}

y = c_{1} cos (6 t) + c_{2} sin (6 t) - \frac{e ^{4 t} cos ^{2} ( 6 t ) + e ^{4 t} sin ^{2} ( 6 t ) + 13 cos ( 6 t ) ln ( sec ( 6 t ) + tan ( 6 t ) )}{26}