(d^2x)/(dt^2)+100x=36cos(8t)

Lösung

\frac{d ^{2} x}{d t ^{2}} + 100 x = 36 cos (8 t)

x = c_{1} cos (10 t) + c_{2} sin (10 t) + cos (8 t)

Schritte zur Lösung

\frac{d ^{2} x}{d t ^{2}} + 100 x = 36 cos (8 t)

Solve linear ODE:

x = c_{1} cos (10 t) + c_{2} sin (10 t) + cos (8 t)

x = c_{1} cos (10 t) + c_{2} sin (10 t) + cos (8 t)

y^{^{''}} - 6 y^{^{'}} + 9 y = t^{- 7} e^{3 t}

x^{^{''}} + 2 x^{^{'}} - 4 x = 6 e^{3 t} - 4 t + 3

y^{^{''}} - 25 y = 3 x^{2} - 2 + e^{x}, y (0) = 1, y^{^{'}} (0) = 0

x^{2} y^{^{''}} - 8 x^{2} y^{^{'}} + 16 x^{2} y = 3 e^{4 x}

y^{^{''}} + 3 y^{^{'}} + 2 y = 12 e^{t}, y (0) = 2, y^{^{'}} (0) = 3