y^{''}+8y^'+2y=cos(x),y(0)=0

Lösung

y^{^{''}} + 8 y^{^{'}} + 2 y = cos (x), y (0) = 0

y = (- c_{2} - \frac{1}{65}) e^{(- 4 + 14) x} + c_{2} e^{(- 4 - 14) x} + \frac{8}{65} sin (x) + \frac{1}{65} cos (x)

Schritte zur Lösung

y^{''} (x) + 8 y^{'} (x) + 2 y = cos (x)

Solve linear ODE:

y = (- c_{2} - \frac{1}{65}) e^{(- 4 + 14) x} + c_{2} e^{(- 4 - 14) x} + \frac{8}{65} sin (x) + \frac{1}{65} cos (x)

y = (- c_{2} - \frac{1}{65}) e^{(- 4 + 14) x} + c_{2} e^{(- 4 - 14) x} + \frac{8}{65} sin (x) + \frac{1}{65} cos (x)

10 x^{^{''}} + 45 x^{^{'}} + 2500 x = 180 cos (7 π)

y^{^{''}} + 7 y^{^{'}} + 12 y = 5 x

\frac{d ^{2} y}{d x ^{2}} - 16 \frac{d y}{d x} - 64 y = 7 e^{8 x}

y^{^{''}} - 11 y^{^{'}} + 24 y = 2, y (0) = 0, y^{^{'}} (0) = 1

y^{^{''}} + 2 y^{^{'}} + 10 y = 10 x + 2