To solve the differential equation 6y + 4cos(x) = 0, we can rearrange it into a more standard form. First, we isolate y:
6y = -4cos(x)
Now, we can solve for y:
y = - rac{4}{6}cos(x)
This simplifies to:
y = - rac{2}{3}cos(x)
Now, the solution we have found represents a particular solution to the differential equation. In a more general context, if there were more terms or a characteristic polynomial to solve, we could use methods like undetermined coefficients or variation of parameters. However, in this specific case, the equation is simple enough for direct manipulation. The final solution we get is the linear function dependent on the cosine of x, scaled by a factor of -2/3.