In problem , solve the equation.
The solution of the given differential equation is .
A first-order ordinary differential equation is referred to as separable if the function in the right-hand side of the equation is expressed as a product of two functions g(x) that is a function of x alone and h(y) that is a function of y alone.
A separable differential equation can be expressed as . By separating the variables, the equation follows . Then, on direct integration of both sides, the solution of the differential equation is determined.
The given equation is
Re-write equation (1) as follows:
After separating the variables, equation (2) can be written as
Integrate both sides of equation (3). It results,
Therefore, the solution of the given equation is .
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