00:01
So here we're given a bunch of functions and asked to match them to the differential equations.
00:05
I'll start with the kind of obvious ones.
00:07
So for e, it's pretty obvious that y prime equals 2y, because when you take the derivative, you get a factor of 2 from the exponent.
00:16
So this matches the equation y prime equals 2 y.
00:19
And on part c, the second derivative of sine is negative sign, meaning that the second derivative plus the initial function is 0, because negative sign of x plus sign of x equals zero.
00:30
So that matches that differential equation.
00:33
Next, we will just go by the differential equation.
00:37
So the first one we'll look at is xy prime minus y equals x squared.
00:42
This one looks like y is probably some sort of polynomial because we're simply taking factors of x and multiplying it by derivatives.
00:51
So we'll try a because that's the simplest polynomial here...