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

Lösung

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

y = c_{1} cos (2 t) + c_{2} sin (2 t) + \frac{- 8 cos ( 2 t ) ln ( tan ( 2 t ) + sec ( 2 t ) ) - e ^{2 t} cos ^{2} ( 2 t ) - e ^{2 t} sin ^{2} ( 2 t )}{8}

Schritte zur Lösung

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

Solve linear ODE:

y = c_{1} cos (2 t) + c_{2} sin (2 t) + \frac{- 8 cos ( 2 t ) ln ( tan ( 2 t ) + sec ( 2 t ) ) - e ^{2 t} cos ^{2} ( 2 t ) - e ^{2 t} sin ^{2} ( 2 t )}{8}

y = c_{1} cos (2 t) + c_{2} sin (2 t) + \frac{- 8 cos ( 2 t ) ln ( tan ( 2 t ) + sec ( 2 t ) ) - e ^{2 t} cos ^{2} ( 2 t ) - e ^{2 t} sin ^{2} ( 2 t )}{8}

y^{^{'''}} - 4 y^{^{''}} + 5 y^{^{'}} - 2 y = 2 e^{- x} + cos (x)

\frac{1}{4} y^{^{''}} + y^{^{''}} + y = x^{2} - 2 x

y^{^{''}} + 3 y^{^{'}} + 2 y = 1, 2 e^{t} y (0) = 2, y^{^{'}} (0) = 3

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

y^{^{''}} + k y = 8 sin (t)