1/6 y^{''}+6y=4tan(6t)-1/2 e^{3t}

Lösung

\frac{1}{6} y^{^{''}} + 6 y = 4 tan (6 t) - \frac{1}{2} e^{3 t}

y = c_{1} cos (6 t) + c_{2} sin (6 t) - \frac{e ^{3 t} cos ^{2} ( 6 t ) + e ^{3 t} sin ^{2} ( 6 t ) + 10 cos ( 6 t ) ln ( sec ( 6 t ) + tan ( 6 t ) )}{15}

Schritte zur Lösung

\frac{1}{6} y^{''} (t) + 6 y = 4 tan (6 t) - \frac{1}{2} e^{3 t}

Solve linear ODE:

y = c_{1} cos (6 t) + c_{2} sin (6 t) - \frac{e ^{3 t} cos ^{2} ( 6 t ) + e ^{3 t} sin ^{2} ( 6 t ) + 10 cos ( 6 t ) ln ( sec ( 6 t ) + tan ( 6 t ) )}{15}

y = c_{1} cos (6 t) + c_{2} sin (6 t) - \frac{e ^{3 t} cos ^{2} ( 6 t ) + e ^{3 t} sin ^{2} ( 6 t ) + 10 cos ( 6 t ) ln ( sec ( 6 t ) + tan ( 6 t ) )}{15}

\frac{d y}{d x} - 1 = y^{2}

\frac{\partial}{\partial x} (x ln (x + 6 y))

y^{^{''}} - 5 y^{^{'}} = e^{5 x}

e x p an d \frac{6}{( w ^{2} - 8 ) ^{4}}

d er i v a t i v e f (x) = 7 e^{- x^{2}}