Differential Equation Question
Hi. I have the equations y= Cx^2 - 2x and y' - 2(y/x)=2, and y(1)=10. The question reads "Verify that y is a general solution of the differential equation. Then find a particular solution of the differential equation that satisfies the given point (1,10)".
I was able to find the particular solution (y=12x^2 - 2x), but was not able to "Verify that y is a general solution of the differential equation".
What I did was have y'=2Cx - 2, and then substituted this into y' - 2 (y/x)=2 to get (2CX-2) - 2y/x =2, making (2Cx^2 - 2y)/(x^2)=4. Where do I go from here?