Question: In Problems 33–40, solve the equation given in:
The solution of the given equation in problem 8 is .
When the equation is of the form, , then the substitution transforms the given equation into a separable equation in the variables v and x.
One has to solve the equation given in problem 7, i.e.,
Rewriting the equation (1) as,
Substitute in equation (2),
Dividing both sides by ,
Therefore, equation (2) becomes,
Separate the variables in equation (3),
Integrating both sides,
The left hand side of the equation (4) can be solved by using partial fraction,
Multiply both sides by ,
Put t = -1 in equation (5),
Therefore, equation (4) becomes,
Put t = 0 in equation (5),
Where, C is the constant of integration.
Put in equation (6),
Hence, the solution of the given equation is .
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