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

解答

\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}

求解步骤

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

求解线性方程:

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}

9 y^{^{''}} - y = x e^{\frac{x}{3}}, y (0) = 1, y (0) = 0

(D^{2} + 1) y = - t

(d^{2} - 4 d + 5) y = (x + 1)^{3}

y^{^{''''}} + 2 y^{^{'''}} + 2 y^{^{''}} + 2 y^{^{'}} + y = x e^{x}

y^{^{''}} - 4 y^{^{'}} + 3 y = (x^{2} - 3 x) e^{x}