(D^2+9)y=81x^2+(14cos(x))

Lösung

(D^{2} + 9) y = 81 x^{2} + (14 cos (x))

y = c_{1} cos (3 x) + c_{2} sin (3 x) + 9 x^{2} - 2 + \frac{7}{4} cos (x)

Schritte zur Lösung

(D^{2} + 9) y = 81 x^{2} + 14 cos (x)

Solve linear ODE:

y = c_{1} cos (3 x) + c_{2} sin (3 x) + 9 x^{2} - 2 + \frac{7}{4} cos (x)

y = c_{1} cos (3 x) + c_{2} sin (3 x) + 9 x^{2} - 2 + \frac{7}{4} cos (x)

y^{^{'''}} - 6 y^{^{''}} + 12 y^{^{'}} - 8 y = t^{- 2} e^{2 t}

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

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

y^{^{''}} + 4 y = t^{2} + 8 e^{t}, y (0) = 0, y^{^{'}} (0) = 7

y^{^{''}} - 4 y = e^{x} cos (x), y (0) = 0.9, y^{^{'}} (0) = - 1.5