Is this what you meant? [tex] \frac{ d\left(y^2\right) }{dx} = 62y -0.2 [/tex]. If so just write z in place of [itex] y^2[/itex] so [tex] \frac{dz}{dx} = 62\sqrt{z} -0.2 [/tex], and separate variables as usual.
Ok, have you learned how to deal with differential equations of the form [tex] y'' + ay' + by = c [/tex] where a,b,c are constants. Because thats what this problem is. If not, I suggest you read through that section in your textbook or notes again. If you do know the theory for diff. eqns of that form, what specifically got you stuck?
That reminds me - this is posted in the wrong section. Please always post requests for help with standard textbook type questions in the homework section, even if it isn't set as homework to you.