y^{''}-2y^'+10y=3e^xtan(3x)

Lösung

y^{^{''}} - 2 y^{^{'}} + 10 y = 3 e^{x} tan (3 x)

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

Schritte zur Lösung

y^{''} (x) - 2 y^{'} (x) + 10 y = 3 e^{x} tan (3 x)

Solve linear ODE:

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

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

y^{^{''}} + 4 y^{^{'}} + 4 y = 7 e^{- 2 t}

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

y^{^{''}} + 8 y^{^{'}} + 2 y = cos (x), y (0) = 0, y^{^{'}} (0) = 1

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

y^{^{''}} - 3 y^{^{'}} + 2 y = 4 x + 6