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

Lösung

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

y = e^{\frac{x}{2}} (c_{1} cos (\frac{3 x}{2}) + c_{2} sin (\frac{3 x}{2})) + \frac{5}{13} sin (2 x) - \frac{12}{13} cos (2 x)

Schritte zur Lösung

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

Solve linear ODE:

y = e^{\frac{x}{2}} (c_{1} cos (\frac{3 x}{2}) + c_{2} sin (\frac{3 x}{2})) + \frac{5}{13} sin (2 x) - \frac{12}{13} cos (2 x)

y = e^{\frac{x}{2}} (c_{1} cos (\frac{3 x}{2}) + c_{2} sin (\frac{3 x}{2})) + \frac{5}{13} sin (2 x) - \frac{12}{13} cos (2 x)

y^{^{'''}} + 4 y^{^{''}} - 9 y^{^{'}} - 36 = x^{2} - 4

y^{^{''}} + y = \frac{1}{( cos ( x ) )}

y^{^{''}} + y = sin (x) + sin (2 x)

y^{^{''}} + 8 y^{^{'}} + 16 y = x

5 y^{^{''}} + 6 y^{^{'}} + 25 y = 3 cos (2 t)