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

Lösung

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

y = c_{1} cos (2 t) + c_{2} sin (2 t) + \frac{- 16 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 = 4 tan (2 t) - \frac{1}{2} e^{2 t}

Solve linear ODE:

y = c_{1} cos (2 t) + c_{2} sin (2 t) + \frac{- 16 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{- 16 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^{^{'}} + 4 y = 2 x + 6, y (0) = 1, y^{^{'}} (0) = \frac{1}{2}

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

y^{^{''}} - 6 y^{^{'}} = 2 x + 1

y^{^{''}} + 3 y^{^{'}} + 2 y = 24 e^{- 2 x}

y^{^{''}} + 100 y = - 2 sin (10 t) - 4 cos (10 t)