# An oddly puzzling differential equation

1. Sep 10, 2009

### iatnogpitw

1. The problem statement, all variables and given/known data
Solve t*y'(t) + 4*y = 0; y(3) = 2. This is the solution---> Ans: y(t) = 162t^(-4)

2. Relevant equations
I need to know how my professor got this answer.

3. The attempt at a solution
I attempted by subtracting 4y to the other side and separated the variables to yield
$$\int(dy/y)$$ = -4$$\int(dt/t)$$
for which you get ln(y) = -4ln(t)
=> y = t*e^(-4).
Can anyone help me on this?
(I left out the constant of integration since that only pertains to part 2 for a particular solution)

2. Sep 10, 2009

### Hurkyl

Staff Emeritus
Are you sure you applied your exponent/logarithm rules correctly?

By the way, the constant of integration is always relevant. Forgetting it is in the same class of mistakes as forgetting that -2 is a solution to x²=4.

3. Sep 10, 2009

### lanedance

have a look at your exponent step

ln(y) = -4ln(t)
now take exponential
eln(y) = y = e-4ln(t)

note - e-4.eln(t)= e-4 + ln(t), not what you have...