In problem 7-16, 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 that is a function of x alone and 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
After separating the variables, equation (1) can be written as
Integrate both sides of equation (2). It results,
Therefore, the solution of the given equation is .
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