y^{''}+6y^'+8y=e^{3x}-sin(x)

Lösung

y^{^{''}} + 6 y^{^{'}} + 8 y = e^{3 x} - sin (x)

y = c_{1} e^{- 2 x} + c_{2} e^{- 4 x} + \frac{1}{35} e^{3 x} - \frac{7}{85} sin (x) + \frac{6}{85} cos (x)

Schritte zur Lösung

y^{''} (x) + 6 y^{'} (x) + 8 y = e^{3 x} - sin (x)

Solve linear ODE:

y = c_{1} e^{- 2 x} + c_{2} e^{- 4 x} + \frac{1}{35} e^{3 x} - \frac{7}{85} sin (x) + \frac{6}{85} cos (x)

y = c_{1} e^{- 2 x} + c_{2} e^{- 4 x} + \frac{1}{35} e^{3 x} - \frac{7}{85} sin (x) + \frac{6}{85} cos (x)

y^{^{''}} + 10 y^{^{'}} + 41 y = t e^{- 5 t} sin (4 t)

y^{^{''}} - y^{^{'}} - 6 y = e^{t}, y (0) = 1, y^{^{'}} (0) = 1

y^{^{''}} - 2 y^{^{'}} + 2 y = e^{2 x} (cos (x) - 4 sin (x))

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

y^{^{''}} - y^{^{'}} + \frac{y}{4} = 3 + e^{\frac{x}{2}}