Implicit Differentiation and understanding the question?

[kyin01]

Hi, I am working on my differential equations excercises and I encountered 2 problems.

First one is, I just wanted to check if I did this implicit differenriation right

Homework Statement

t^{2} \bullet y +y^{2} = C where is is a constant

The Attempt at a Solution

My solution is
y \bullet \frac{dy}{dt} * (2t+2)=0



My 2nd question is understanding the question of the problem.
Its phrased like this:
"Find values of m so that y=exp(mx) is a solution of y'+2y=0"

I'm not sure exactly what to do, I've tried plugging in y=exp(mx) directly into the differential equation but I'm not sure what to do next. I've also tried solving the differential equation but I don't know where to go from there.
Any tips?


Thanks for your time.

 

[rock.freak667]

Hi, I am working on my differential equations excercises and I encountered 2 problems.

First one is, I just wanted to check if I did this implicit differenriation right

Homework Statement

t^{2} \bullet y +y^{2} = C where is is a constant

The Attempt at a Solution

My solution is
y \bullet \frac{dy}{dt} * (2t+2)=0

I didn't check this one through but, I will assume you used the product rule for t²y

My 2nd question is understanding the question of the problem.
Its phrased like this:
"Find values of m so that y=exp(mx) is a solution of y'+2y=0"

I'm not sure exactly what to do, I've tried plugging in y=exp(mx) directly into the differential equation but I'm not sure what to do next. I've also tried solving the differential equation but I don't know where to go from there.
Any tips?


Thanks for your time.

yes plug it into the equation, and since e^mx≠ 0 for all x, you can divide by it