Differential Equations: If y(1) =3 then y(1/2) = ?

[Northbysouth]

Homework Statement

If y satisfies the differential equation:

ty'(t) + tln(t)y(t) = 0

and y(1) = 3 then y(1/2) = ?

I have attached an image of the question with the possible solutions:

Homework Equations

The Attempt at a Solution

Initially I tried plugging in t=1 and y(1) = 3 giving me:

y'(1)+3ln(1) = 0

Hence y'(1) = 0

I did the same for t=1/2

1/2[y'(1/2) + ln(1/2)y(1/2)] = 0

But this doesn't seem to help me. Any suggestions would be appreciated.

 

[LCKurtz]

Why don't you just solve the DE and put in the boundary conditions? It looks to be separable and linear so you have a couple of options.

 

[SammyS]

Homework Statement

If y satisfies the differential equation:

ty'(t) + tln(t)y(t) = 0

and y(1) = 3 then y(1/2) = ?

I have attached an image of the question with the possible solutions:

Homework Equations

The Attempt at a Solution

Initially I tried plugging in t=1 and y(1) = 3 giving me:

y'(1)+3ln(1) = 0

Hence y'(1) = 0

I did the same for t=1/2

1/2[y'(1/2) + ln(1/2)y(1/2)] = 0

But this doesn't seem to help me. Any suggestions would be appreciated.

To help you solve the D.E., factor out t .