1. The problem is to solve the differential equation for $x$. 2. Since the exact differential equation is not provided, let's consider a general first-order differential equation of the form $$\frac{dx}{dt} = f(t,x).$$ 3. To solve for $x$, we typically separate variables if possible or use an integrating factor or other methods depending on the form of $f(t,x)$. 4. For example, if the equation is separable: $$\frac{dx}{dt} = g(t)h(x),$$ we rewrite as $$\frac{1}{h(x)} dx = g(t) dt$$ and integrate both sides. 5. After integration, solve the resulting equation for $x$ explicitly if possible. 6. Without the specific differential equation, this is the general approach to solve for $x$. 7. Please provide the exact differential equation for a detailed step-by-step solution.