## For the first problem:

x = (y^2 + 3y)^(1/3)

To solve for y explicitly, you can rearrange the equation as follows:

x^3 = y^2 + 3y

Now, you can treat this as a quadratic equation in terms of y. Use the quadratic formula:

y = (-b +/- sqrt(b^2 - 4ac))/(2a)

In this case, a = 1, b = 3, and c = -x^3. Substituting these values into the formula, you get:

y = (-3 +/- sqrt(9 + 4x^3))/2

So, the explicit solution for y is:

y = (-3 +/- sqrt(9 + 4x^3))/2

For the second problem:

x = 1/[(y^2 + 3y - 5)^3]

To solve for y explicitly, you can follow a similar process. Start by rearranging the equation:

1/x = (y^2 + 3y - 5)^3

Take the cube root of both sides:

(1/x)^(1/3) = y^2 + 3y - 5

Now, you have a quadratic equation in terms of y. Use the quadratic formula:

y = (-b +/- sqrt(b^2 - 4ac))/(2a)

In this case, a = 1, b = 3, and c = -5 - (1/x)^(1/3). Substituting these values into the formula, you get:

y = (-3 +/- sqrt(9 + 4(5 + (1/x)^(1/3))))/2

Note that the expression (1/x)^(1/3) can be simplified depending on the value of x.

So, the explicit solution for y is:

y = (-3 +/- sqrt(9 + 4(5 + (1/x)^(1/3))))/2