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

Lösung

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

y = c_{1} cos (2 t) + c_{2} sin (2 t) + \frac{- 45 cos ( 2 t ) ln ( tan ( 2 t ) + sec ( 2 t ) ) - e ^{4 t} cos ^{2} ( 2 t ) - e ^{4 t} sin ^{2} ( 2 t )}{30}

Schritte zur Lösung

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

Solve linear ODE:

y = c_{1} cos (2 t) + c_{2} sin (2 t) + \frac{- 45 cos ( 2 t ) ln ( tan ( 2 t ) + sec ( 2 t ) ) - e ^{4 t} cos ^{2} ( 2 t ) - e ^{4 t} sin ^{2} ( 2 t )}{30}

y = c_{1} cos (2 t) + c_{2} sin (2 t) + \frac{- 45 cos ( 2 t ) ln ( tan ( 2 t ) + sec ( 2 t ) ) - e ^{4 t} cos ^{2} ( 2 t ) - e ^{4 t} sin ^{2} ( 2 t )}{30}

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

y^{^{''}} - 3 y^{^{'}} + 3 y^{^{'}} - y = x - 8 e^{x}

y^{^{''}} + 100 y^{^{'}} + \frac{1}{0.0004} y = 30, y (0) = 0

y^{^{''''}} - 5 y^{^{'''}} + 4 y^{^{''}} = x

2 y^{^{''}} + y = 5 + cos (4 t)