y^{''}-10y^'+25y=xcos(5x)

Lösung

y^{^{''}} - 10 y^{^{'}} + 25 y = x cos (5 x)

y = c_{1} e^{5 x} + c_{2} x e^{5 x} - \frac{x sin ( 5 x )}{50} - \frac{1}{250} sin (5 x) - \frac{1}{250} cos (5 x)

Schritte zur Lösung

y^{''} (x) - 10 y^{'} (x) + 25 y = x cos (5 x)

Solve linear ODE:

y = c_{1} e^{5 x} + c_{2} x e^{5 x} - \frac{x sin ( 5 x )}{50} - \frac{1}{250} sin (5 x) - \frac{1}{250} cos (5 x)

y = c_{1} e^{5 x} + c_{2} x e^{5 x} - \frac{x sin ( 5 x )}{50} - \frac{1}{250} sin (5 x) - \frac{1}{250} cos (5 x)

y^{^{''}} + 9 y = 3 x, y (0) = 1, y^{^{'}} (0) = 3

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

y^{^{''}} - 35 y^{^{'}} + 9 y = 60 t, y (0) = - 1, y^{^{'}} (0) = 2

y^{^{''}} + 2 y^{^{'}} + 5 y = 52 cos (3 x)

y^{^{''}} - 5 y^{^{'}} - 24 y = 5 + 2 t