Sovle by separation of variables dy/dx= (x+1)^2.

Given differential equation is:

(1)

We can separate the variables as follows:

(2)

Now, we can integrate both sides of the equation:

(3)

Integrating the left-hand side requires the substitution and , yielding:

(4)

where is the constant of integration.

For the right-hand side, we can simply integrate with respect to to obtain:

(5)

where is another constant of integration.

Substituting back , we have:

(6)

Simplifying and solving for , we get:

(7)

where is the constant of integration.

Therefore, the solution to the differential equation is:

(8)

where is the constant of integration.