y^{''}+3y^'+33y=9cos(5x)

Lösung

y^{^{''}} + 3 y^{^{'}} + 33 y = 9 cos (5 x)

y = e^{- \frac{3 x}{2}} (c_{1} cos (\frac{123 x}{2}) + c_{2} sin (\frac{123 x}{2})) + \frac{135}{289} sin (5 x) + \frac{72}{289} cos (5 x)

Schritte zur Lösung

y^{''} (x) + 3 y^{'} (x) + 33 y = 9 cos (5 x)

Solve linear ODE:

y = e^{- \frac{3 x}{2}} (c_{1} cos (\frac{123 x}{2}) + c_{2} sin (\frac{123 x}{2})) + \frac{135}{289} sin (5 x) + \frac{72}{289} cos (5 x)

y = e^{- \frac{3 x}{2}} (c_{1} cos (\frac{123 x}{2}) + c_{2} sin (\frac{123 x}{2})) + \frac{135}{289} sin (5 x) + \frac{72}{289} cos (5 x)

4 y^{^{''}} - 4 y^{^{'}} + y = (- 3 x + 4) sin (x)

y^{^{''}} + y^{^{'}} - 6 = 0

y^{^{''}} - 2 y^{^{'}} + 65 y = e^{x} cos (8 x)

x^{^{''}} + 8 x = 16 cos (4 t)

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