I'm confused with this particular question, so could someone please explain how to go about doing a question such as this one?

I want to place the following equation in a form suitable for using the integrating factor method: $$(x-3)\frac{dy}{dx}-y=(x-3)^2$$

I want to solve the above differential equation given $y=10$ when $x=5$.

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    $\begingroup$ can you use $\LaTeX$ please? $\endgroup$ – Dr. Sonnhard Graubner Oct 5 '16 at 10:49
  • $\begingroup$ is it $$\frac{dy}{dx}-y=(x-3)^2$$? $\endgroup$ – Dr. Sonnhard Graubner Oct 5 '16 at 10:50
  • $\begingroup$ sorry about that and its $$(x-3)\frac{dy}{dx}-y=(3-x)^2$$ $\endgroup$ – Kirn Johnson Oct 5 '16 at 11:23
  • $\begingroup$ the thing is i dont understand how to go about doing such question in general i missed the class due to work (PT student) and i was hoping i would be given an explanation on how to go about doing the questions i asked i.e put it in the form and solve $\endgroup$ – Kirn Johnson Oct 5 '16 at 12:11

for the particular solution make the ansatz $$y_p(x)=ax^2+bx+c$$ with $a,b,c$ real numbers. the solution is given by $$y=x(x-3)+C(x-3)$$


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