y^{''}+y^'+64y=cos(2x)

Lösung

y^{^{''}} + y^{^{'}} + 64 y = cos (2 x)

y = e^{- \frac{x}{2}} (c_{1} cos (\frac{255 x}{2}) + c_{2} sin (\frac{255 x}{2})) + \frac{1}{1802} sin (2 x) + \frac{15}{901} cos (2 x)

Schritte zur Lösung

y^{''} (x) + y^{'} (x) + 64 y = cos (2 x)

Solve linear ODE:

y = e^{- \frac{x}{2}} (c_{1} cos (\frac{255 x}{2}) + c_{2} sin (\frac{255 x}{2})) + \frac{1}{1802} sin (2 x) + \frac{15}{901} cos (2 x)

y = e^{- \frac{x}{2}} (c_{1} cos (\frac{255 x}{2}) + c_{2} sin (\frac{255 x}{2})) + \frac{1}{1802} sin (2 x) + \frac{15}{901} cos (2 x)

d (x) = 4 x^{7} + 10 x^{6} + 5 x - 2 (2 x^{7} + 5 x^{6} + 10)

2 \frac{d ^{2} y}{d x ^{2}} + 2 \frac{d y}{d x} + 3 y = x^{2} + 2 x - 1

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

y^{^{''}} + 49 y = x^{2} cos (7 x) + x e^{- 7 x}

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