Question

Please help. How do I separate the variables in the following differential equation dy/dx=(2/27)(x-3)then square root (x^2-6x+23)/y where (y>0). Then give general solution in implicit form. Thank you so much if you can help.

Answer 1

Check if the initial equation is the following:

dy/dx=(2/27)(x-3)√((x^2-6x+23)/y)

27√(y) dy = 2(x-3)√(x^2-6x+23)dx

Integrate both sides and express y in implicit form.