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

Lösung

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

y = c_{1} e^{x} + c_{2} x e^{x} + x + sin (x)

Schritte zur Lösung

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

Solve linear ODE:

y = c_{1} e^{x} + c_{2} x e^{x} + x + sin (x)

y = c_{1} e^{x} + c_{2} x e^{x} + x + sin (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)

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