An oddly puzzling differential equation

[iatnogpitw]

Homework Statement

Solve t*y'(t) + 4*y = 0; y(3) = 2. This is the solution---> Ans: y(t) = 162t^(-4)

Homework Equations

I need to know how my professor got this answer.

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)

 

[Hurkyl]

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.

 

[lanedance]

have a look at your exponent step

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

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