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

Lösung

linear

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

y = c_{1} cos (4 t) + c_{2} sin (4 t) + \frac{- 75 cos ( 4 t ) ln ( sec ( 4 t ) + tan ( 4 t ) ) - 16 e ^{3 t} cos ^{2} ( 4 t ) - 16 e ^{3 t} sin ^{2} ( 4 t )}{300}

Schritte zur Lösung

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

Solve linear ODE:

y = c_{1} cos (4 t) + c_{2} sin (4 t) + \frac{- 75 cos ( 4 t ) ln ( sec ( 4 t ) + tan ( 4 t ) ) - 16 e ^{3 t} cos ^{2} ( 4 t ) - 16 e ^{3 t} sin ^{2} ( 4 t )}{300}

y = c_{1} cos (4 t) + c_{2} sin (4 t) + \frac{- 75 cos ( 4 t ) ln ( sec ( 4 t ) + tan ( 4 t ) ) - 16 e ^{3 t} cos ^{2} ( 4 t ) - 16 e ^{3 t} sin ^{2} ( 4 t )}{300}

2 y^{^{'''}} - 2 y^{^{'}} = - 3 t^{2} - 4 t

y^{^{'''}} - 2 y^{^{''}} + y^{^{'}} = 3 t^{2} - 18

y^{^{''}} + 8 y^{^{'}} + 2 y = cos (x), y (0) = 0

10 x^{^{''}} + 45 x^{^{'}} + 2500 x = 180 cos (7 π)

y^{^{''}} + 7 y^{^{'}} + 12 y = 5 x