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Dividing both sides of the initial equation by 3x and multiplying both sides by dx gives the equation:
dy = (sqrt(x^2-25)/(3x))dx
This equation can be integrated leaving the equation:
y = (1/9)(sqrt(x^2-25)^(3/2)) + C.
Plugging in the point (5,3) means C = 3 so the final answer is:
y = (1/9)(sqrt(x^2-25)^(3/2)) + 3
Please let me know if you need any clarification. I'm always happy to answer your questions.
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