1/2 y^{''}+2y=4tan(2t)-1/3 e^t

解

\frac{1}{2} y^{^{''}} + 2 y = 4 tan (2 t) - \frac{1}{3} e^{t}

y = c_{1} cos (2 t) + c_{2} sin (2 t) + \frac{- 30 cos ( 2 t ) ln ( sec ( 2 t ) + tan ( 2 t ) ) - 2 e ^{t} cos ^{2} ( 2 t ) - 2 e ^{t} sin ^{2} ( 2 t )}{15}

解答ステップ

\frac{1}{2} y^{''} (t) + 2 y = 4 tan (2 t) - \frac{1}{3} e^{t}

線形 ODE を解く:

y = c_{1} cos (2 t) + c_{2} sin (2 t) + \frac{- 30 cos ( 2 t ) ln ( sec ( 2 t ) + tan ( 2 t ) ) - 2 e ^{t} cos ^{2} ( 2 t ) - 2 e ^{t} sin ^{2} ( 2 t )}{15}

y = c_{1} cos (2 t) + c_{2} sin (2 t) + \frac{- 30 cos ( 2 t ) ln ( sec ( 2 t ) + tan ( 2 t ) ) - 2 e ^{t} cos ^{2} ( 2 t ) - 2 e ^{t} sin ^{2} ( 2 t )}{15}