y^{'''}=3y^{''}+9(e^{2x})+5(cos(x))

Lösung

y^{^{'''}} = 3 y^{^{''}} + 9 (e^{2 x}) + 5 (cos (x))

y = c_{1} e^{3 x} + c_{2} + c_{3} x - \frac{9}{4} e^{2 x} - \frac{1}{2} sin (x) + \frac{3}{2} cos (x)

Schritte zur Lösung

y^{'''} (x) = 3 y^{''} (x) + 9 (e^{2 x}) + 5 (cos (x))

Solve linear ODE:

y = c_{1} e^{3 x} + c_{2} + c_{3} x - \frac{9}{4} e^{2 x} - \frac{1}{2} sin (x) + \frac{3}{2} cos (x)

y = c_{1} e^{3 x} + c_{2} + c_{3} x - \frac{9}{4} e^{2 x} - \frac{1}{2} sin (x) + \frac{3}{2} cos (x)

y^{^{''}} + 7 y^{^{'}} + 10 y = 7 u

y^{^{''}} + 4 y = cos (x), y (0) = 0, y^{^{'}} (0) = 0

2 y^{^{''}} + y^{^{'}} = 3 x^{2} + 10 x

3 y^{^{''}} + 2 (9.81)^{2} y = 49 (9.81) cos (8 t)

y^{^{''}} - 4 y^{^{'}} = 2 x - 1