In its normal form, you do not solve differential equation for x, but for a function of x, usually denoted by y = f(x).
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Another method to solve differential equation is taking y and dy terms on one side, and x and dy terms on other side, then integrating on both sides.This is a general solution. So if we want to particular solution we choose initial conditions.
I assume that you mean that you are given a differential equation dy/dx and want to solve it. If that is the case, then you would multiply by dx on both sides and then integrate both the left and right sides of the equation.
There is no equation to solve, only an expression.
What is integrating factor of linear differential equation? Ans: assume y = y(x) in the given linear ODE. Then, by an integrating factor of this ODE, we mean a function g(x) such that upon multiplying the ODE by g(x), it is transformed into an exact differential of the nform d[f(x)] = 0.
To solve an equation for x, you need to isolate the variable on one side of the equation. Start by performing the inverse operation to undo any addition, subtraction, multiplication, or division. Once you have x by itself, the solution will be the value of x that satisfies the equation. Remember to follow the order of operations and be careful with signs to ensure accuracy in your answer.