1/6 y^{''}+6y=2tan(6t)-1/3 e^t

Lösung

\frac{1}{6} y^{^{''}} + 6 y = 2 tan (6 t) - \frac{1}{3} e^{t}

y = c_{1} cos (6 t) + c_{2} sin (6 t) + \frac{- 37 cos ( 6 t ) ln ( sec ( 6 t ) + tan ( 6 t ) ) - 6 e ^{t} cos ^{2} ( 6 t ) - 6 e ^{t} sin ^{2} ( 6 t )}{111}

Schritte zur Lösung

\frac{1}{6} y^{''} (t) + 6 y = 2 tan (6 t) - \frac{1}{3} e^{t}

Solve linear ODE:

y = c_{1} cos (6 t) + c_{2} sin (6 t) + \frac{- 37 cos ( 6 t ) ln ( sec ( 6 t ) + tan ( 6 t ) ) - 6 e ^{t} cos ^{2} ( 6 t ) - 6 e ^{t} sin ^{2} ( 6 t )}{111}

y = c_{1} cos (6 t) + c_{2} sin (6 t) + \frac{- 37 cos ( 6 t ) ln ( sec ( 6 t ) + tan ( 6 t ) ) - 6 e ^{t} cos ^{2} ( 6 t ) - 6 e ^{t} sin ^{2} ( 6 t )}{111}

y^{^{''}} - y^{^{'}} - 2 y = e^{x} cos (x)

y^{^{''}} + 4 y = \frac{t}{2} - \frac{t cos ( 2 t )}{2}

y^{^{''}} - 7 y^{^{'}} - 8 y = 8 x^{2} - 2 x

y^{^{''}} + 16 y = cos (4 t), y (0) = 3, y^{^{'}} (0) = 2

3 \frac{d ^{2} y}{d x ^{2}} + 20 \frac{d y}{d x} + 25 y = cos (2 x)