1/6 y^{''}+6y=3tan(6t)-1/3 e^{4t}

Lösung

\frac{1}{6} y^{^{''}} + 6 y = 3 tan (6 t) - \frac{1}{3} e^{4 t}

y = c_{1} cos (6 t) + c_{2} sin (6 t) - \frac{e ^{4 t} cos ^{2} ( 6 t ) + e ^{4 t} sin ^{2} ( 6 t ) + 13 cos ( 6 t ) ln ( sec ( 6 t ) + tan ( 6 t ) )}{26}

Schritte zur Lösung

\frac{1}{6} y^{''} (t) + 6 y = 3 tan (6 t) - \frac{1}{3} e^{4 t}

Solve linear ODE:

y = c_{1} cos (6 t) + c_{2} sin (6 t) - \frac{e ^{4 t} cos ^{2} ( 6 t ) + e ^{4 t} sin ^{2} ( 6 t ) + 13 cos ( 6 t ) ln ( sec ( 6 t ) + tan ( 6 t ) )}{26}

y = c_{1} cos (6 t) + c_{2} sin (6 t) - \frac{e ^{4 t} cos ^{2} ( 6 t ) + e ^{4 t} sin ^{2} ( 6 t ) + 13 cos ( 6 t ) ln ( sec ( 6 t ) + tan ( 6 t ) )}{26}

y^{^{''}} - 4 y^{^{'}} + 8 y = x e^{x}

y^{^{''}} - 2 y^{^{'}} + 2 y = x + 1, y (0) = 3, y^{^{'}} (0) = 0

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

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

\frac{d ^{2} x}{d t ^{2}} + 36 x = 10 sin (4 t), x (0) = 0