y^{''}-y^'-6y=51cos(3x)

Lösung

y^{^{''}} - y^{^{'}} - 6 y = 51 cos (3 x)

y = c_{1} e^{3 x} + c_{2} e^{- 2 x} - \frac{17}{26} sin (3 x) - \frac{85}{26} cos (3 x)

Schritte zur Lösung

y^{''} (x) - y^{'} (x) - 6 y = 51 cos (3 x)

Solve linear ODE:

y = c_{1} e^{3 x} + c_{2} e^{- 2 x} - \frac{17}{26} sin (3 x) - \frac{85}{26} cos (3 x)

y = c_{1} e^{3 x} + c_{2} e^{- 2 x} - \frac{17}{26} sin (3 x) - \frac{85}{26} cos (3 x)

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

y^{^{''}} + 16 y^{^{'}} + 100 y = 10, y (0) = 0, y^{^{'}} (0) = 0

y^{^{''}} + π^{2} y = \frac{5}{ln ( 10 )} sin (x ln (2))

\frac{d ^{2} y}{d t ^{2}} + 6 \frac{d y}{d t} + 9 y = e^{- 3 t}

y^{^{''}} + 2 y^{^{'}} + y = \frac{1}{x} e^{- x}