Help me on number problem 4 please
2 answers:
Let J be the number of points Jaylen scored, and T be the number of points Trevor scored. We have two pieces of information, which are enough to determine the values of the unknowns, because there are two of them (you need as many equations as unknowns).
The first thing we're told is that they scored 485 together, so you have
Then we know that Jaylen scored 25 points less than Trevor, which means
Substitute this expression for J in the first equation to get
So, now that we know that Trevor scored 255 points, we can easily calculate Jaylen's score:
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Given a solution 
, we can attempt to find another via reduction of order of the form 
. This has derivatives
Substituting into the ODE yields
Now letting
, so that 
, you end up with the ODE linear in 
Assuming
(which is reasonable, since 
is a singular point), you can divide through by 
and end up with
and integrating both sides with respect to
gives
Back-substitute to solve for
:
and again to solve for
:
Alternatively, you can solve this ODE from scratch by employing the Euler substitution (which works because this equation is of the Cauchy-Euler type),
. You'll arrive at the same solution, but it doesn't hurt to know there's more than one way to solve this.
Substituting into the ODE yields
Now letting
Assuming
and integrating both sides with respect to
Back-substitute to solve for
and again to solve for
Alternatively, you can solve this ODE from scratch by employing the Euler substitution (which works because this equation is of the Cauchy-Euler type),