Solve the nonlinear differential equations in Exercises 6through 11 using the method of separation of variables:Write the differential equation as and integrate both sides.
The solution is .
Consider the equation as follows.
Now, separate the variables as follows.
Integrating on both sides as follows.
Simplify further as follows:
Substituting the initial condition as follows.
Now, substitute the value for in as follows:
Simplify further as follows.
Now, squaring on both sides as follows:
Hence, the solution for the differential equation is .
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