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

Lösung

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

y = c_{1} cos (6 t) + c_{2} sin (6 t) + \frac{- 15 cos ( 6 t ) ln ( tan ( 6 t ) + sec ( 6 t ) ) - 4 e ^{3 t} cos ^{2} ( 6 t ) - 4 e ^{3 t} sin ^{2} ( 6 t )}{90}

Schritte zur Lösung

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

Solve linear ODE:

y = c_{1} cos (6 t) + c_{2} sin (6 t) + \frac{- 15 cos ( 6 t ) ln ( tan ( 6 t ) + sec ( 6 t ) ) - 4 e ^{3 t} cos ^{2} ( 6 t ) - 4 e ^{3 t} sin ^{2} ( 6 t )}{90}

y = c_{1} cos (6 t) + c_{2} sin (6 t) + \frac{- 15 cos ( 6 t ) ln ( tan ( 6 t ) + sec ( 6 t ) ) - 4 e ^{3 t} cos ^{2} ( 6 t ) - 4 e ^{3 t} sin ^{2} ( 6 t )}{90}

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

y^{^{''}} - 5 y^{^{'}} + 4 y = 1

y^{^{''}} - 100 y = 9 t^{2} e^{10 t}

y^{^{''}} - 16 y = cosh (4 x)

y^{^{''}} + 9 y = \frac{csc ( 3 x )}{4}