y^{''}-9y=(x^2-9)sin(3x)

Lösung

y^{^{''}} - 9 y = (x^{2} - 9) sin (3 x)

y = c_{1} e^{3 x} + c_{2} e^{- 3 x} - \frac{x ^{2} sin ( 3 x )}{18} - \frac{x cos ( 3 x )}{27} + \frac{41}{81} sin (3 x)

Schritte zur Lösung

y^{''} (x) - 9 y = (x^{2} - 9) sin (3 x)

Solve linear ODE:

y = c_{1} e^{3 x} + c_{2} e^{- 3 x} - \frac{x ^{2} sin ( 3 x )}{18} - \frac{x cos ( 3 x )}{27} + \frac{41}{81} sin (3 x)

y = c_{1} e^{3 x} + c_{2} e^{- 3 x} - \frac{x ^{2} sin ( 3 x )}{18} - \frac{x cos ( 3 x )}{27} + \frac{41}{81} sin (3 x)

y^{^{''}} - 36 y = 8, y (0) = 1, y^{^{'}} (0) = 0

y^{^{'''}} - 36 y^{^{'}} = t e^{- 6 t} + 7 cos (6 t)

2 y^{^{''}} + 3 y^{^{'}} + y = g (t)

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

(D^{2} - 1) y = (1 + e^{- x})^{- 2}