Use reduction of Order to find second solution.
t^2y''+2ty'-2y=0 y1(t)=t

Question

Use reduction of Order to find second solution.
t^2y''+2ty'-2y=0               y1(t)=t

anonymous · Answer

I think u put y' = x  ->  y'' = 1 and y = x^2/2 + c

Then use the condition to calculate c. etc

anonymous · Answer

um what? this is Differential Equations

anonymous · Answer

Yes, I am reducing to two first order de's....

anonymous · Answer

o well thats wrong y2'= v'(t) +v(t)

anonymous · Answer

?

anonymous · Answer

thats now how you solve reduction of order problems, you DONT need to split them up into 2 1st order Diff EQs

anonymous · Answer

OK

anonymous · Answer

Now I see, y1(t) = t is a solution, not an initial condition....duh.

anonymous · Answer

So u have put y2 = v(t)t ->

y2'= v'(t) +v(t)

Is this where the problem is?

anonymous · Answer

After subbing in the DE and simplifying I got

t^3v'' +4t^2v' = 0 and putting w =v' (so w' =v'') ->

t^3w' +4t^2w for a first order de.