To solve this differential equation, we can use the method of separation of variables.

Given:

у' = 2 cos(x/2 + 1)
у' = 4/(3x-1)^2

We can set the derivatives equal to each other:

2 cos(x/2 + 1) = 4/(3x-1)^2

Now, we can separate the variables by joining like terms:

2 cos(x/2 + 1) dx = 4/(3x-1)^2 dy

Next, we integrate both sides with respect to their corresponding variables:

∫ 2 cos(x/2 + 1) dx = ∫ 4/(3x-1)^2 dy

Integrating the left side yields:

2 ∫ cos(x/2 + 1) dx = 2 sin(x/2 + 1) + C1

Integrating the right side yields:

∫ 4/(3x-1)^2 dy = -4/(3x-1) + C2

Setting these two results equal to each other, we have:

2 sin(x/2 + 1) + C1 = -4/(3x-1) + C2

Where C1 and C2 are arbitrary constants.

This is the general solution to the given differential equation.