(a)
The solution for
(a)
Answer to Problem 12.1P
The solution for
Explanation of Solution
Given nonlinear first-order equation,
Separating same variables in one side of the equation
Integrate the above equation and solving
Here,
Squaring on both sides
Let,
Conclusion:
Therefore, the solution for
(b)
Show that there is another solution for
(b)
Answer to Problem 12.1P
The another solution for
Explanation of Solution
Assume
Substitute
Since,
Conclusion:
The another solution for
(c)
Show that although
(c)
Answer to Problem 12.1P
It is shown that
Explanation of Solution
From part (a), the solution for
Now, consider
Substitute
Differentiate the above equation with respect to
Now, substitute
Substitute the above equation in
Thus,
From part (b), the solution for
Now, consider
Substitute
Differentiate the above equation with respect to
Now, substitute
Substitute the above equation in
Thus,
Now, consider
Substitute
Differentiate the above equation with respect to
Now, substitute
Substitute the above equation in
Thus,
Conclusion:
It is shown that
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