y^{''}-6y^'+15y=2sin(3x)

Lösung

y^{^{''}} - 6 y^{^{'}} + 15 y = 2 sin (3 x)

y = e^{3 x} (c_{1} cos (6 x) + c_{2} sin (6 x)) + \frac{1}{30} sin (3 x) + \frac{1}{10} cos (3 x)

Schritte zur Lösung

y^{''} (x) - 6 y^{'} (x) + 15 y = 2 sin (3 x)

Solve linear ODE:

y = e^{3 x} (c_{1} cos (6 x) + c_{2} sin (6 x)) + \frac{1}{30} sin (3 x) + \frac{1}{10} cos (3 x)

y = e^{3 x} (c_{1} cos (6 x) + c_{2} sin (6 x)) + \frac{1}{30} sin (3 x) + \frac{1}{10} cos (3 x)

y^{^{''}} - y + x = 0

D (p) = \frac{350}{p}

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

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

y^{^{''}} + 3 \cdot y^{^{'}} = 2