x^{''}+8x=16cos(4t)

Lösung

x^{^{''}} + 8 x = 16 cos (4 t)

x = c_{1} cos (2^{1 + \frac{1}{2}} t) + c_{2} sin (2^{1 + \frac{1}{2}} t) - 2 cos (4 t)

Schritte zur Lösung

x^{''} (t) + 8 x = 16 cos (4 t)

Solve linear ODE:

x = c_{1} cos (2^{1 + \frac{1}{2}} t) + c_{2} sin (2^{1 + \frac{1}{2}} t) - 2 cos (4 t)

x = c_{1} cos (2^{1 + \frac{1}{2}} t) + c_{2} sin (2^{1 + \frac{1}{2}} t) - 2 cos (4 t)

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

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

4 y^{^{''}} - 4 y^{^{'}} + y = 64 e^{\frac{t}{2}}

5 y^{^{''}} + y = - 6 x

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