y^{''}-2y^'+2y=4e^xcos(x)

Lösung

y^{^{''}} - 2 y^{^{'}} + 2 y = 4 e^{x} cos (x)

y = e^{x} (c_{1} cos (x) + c_{2} sin (x)) + 2 e^{x} x sin (x)

Schritte zur Lösung

y^{''} (x) - 2 y^{'} (x) + 2 y = 4 e^{x} cos (x)

Solve linear ODE:

y = e^{x} (c_{1} cos (x) + c_{2} sin (x)) + 2 e^{x} x sin (x)

y = e^{x} (c_{1} cos (x) + c_{2} sin (x)) + 2 e^{x} x sin (x)

y^{^{''}} + 2 y^{^{'}} - 5 y = - 2

4 y^{^{''}} + 16 y = 1, y (0) = - 2, y^{^{'}} (0) = 0

y^{^{''}} + y = t^{3}

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

y^{^{''}} - 6 y^{^{'}} + 9 y = e^{x}