Question: Integro-Diff-Eq steps to solution

For the following Equation:

Equation := int(diff(u(x), x)*v(x), x) = int(u(x)^(1/2)*v(x), x)^(-2/3);
Maplesoft finds the following solution:

Solution1:=3/4*u(x)^(4/3) + 2/3*u(x)^(5/6)*Intat(1/(sqrt(u(x))*Int(v(_b), _b))^(5/3), _b = x) + _C1 = 0

or , which I believe as an alternative, can be written as

Solution2:=3/4*u(x)^(4/3) + 2/3*u(x)^(5/6)*Int(1/(sqrt(u(x))*Int(v(x),x))^(5/3) +_C1=0

My question is how did Maple arrive at 'Solution1' from 'Equation'? In other words, can someone fill

in the steps between 'Equation'  and 'Solution1'? Or even, prove that Solution 1 is a valid solution to Equation.

Plugging the Solution1 into Equation, did not clearly demonstate the validity of the solution (to me at least)

Unfortunately, I am still unable to post the corresponding Maplesoft worksheet onto this post.

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