Differential calculus.

Having trouble grasping the basic concepts of this class.

GUESS one function y(t) which solves the problem below, by determining the general form the function might take and then evaluating some coefficients.
7 t (dy/dt) + y = t^2

Question

Differential calculus.

Having trouble grasping the basic concepts of this class.

GUESS one function y(t) which solves the problem below, by determining the general form the function might take and then evaluating some coefficients. 
7 t (dy/dt) + y = t^2

anonymous · Answer

I think my first step is to get the y's and dy on one side, and the t's and dt on the other

anonymous · Answer

$$(7/y) dy = t - (1/t) dt$$

zarkon · Answer

try   $y=at^2$

anonymous · Answer

From the start or where I left off?

anonymous · Answer

From the start.  A good guess for the function is some power of t, 
$$y(t) = a\cdot t^b $$
If you plug that in, you'll find that $b=2$ as Zarkon said, but you'll also find what $a$ has to be.