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

Lösung

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

y = c_{1} cos (4 t) + c_{2} sin (4 t) + \frac{- 5 cos ( 4 t ) ln ( tan ( 4 t ) + sec ( 4 t ) ) - 2 e ^{2 t} cos ^{2} ( 4 t ) - 2 e ^{2 t} sin ^{2} ( 4 t )}{20}

Schritte zur Lösung

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

Solve linear ODE:

y = c_{1} cos (4 t) + c_{2} sin (4 t) + \frac{- 5 cos ( 4 t ) ln ( tan ( 4 t ) + sec ( 4 t ) ) - 2 e ^{2 t} cos ^{2} ( 4 t ) - 2 e ^{2 t} sin ^{2} ( 4 t )}{20}

y = c_{1} cos (4 t) + c_{2} sin (4 t) + \frac{- 5 cos ( 4 t ) ln ( tan ( 4 t ) + sec ( 4 t ) ) - 2 e ^{2 t} cos ^{2} ( 4 t ) - 2 e ^{2 t} sin ^{2} ( 4 t )}{20}

y^{^{''''}} + 2 y^{^{''}} + y = 11 + cos (3 t)

y^{^{''}} + 4 y = sin (3 t), y (0) = 1, y^{^{'}} (0) = 0

y^{^{''}} - 2 y^{^{'}} - 3 y = 12 e x - 6

y^{^{''}} - 2 y^{^{'}} - 3 y = 12 e x - 9

y^{^{''}} + 2 y^{^{'}} + 4 y = \frac{x}{e ^{2 x} ( 1 + x ^{2} )}