Differential equation: dy/dx = e^(8x-3y), y(0)=16

[Lo.Lee.Ta.]

1. The next differential equation I'm working on is this:

dy/dx= e^{8x - 3y}

Alright, I thought to cancel out the e, we could take the ln of both sides...?

ln(dy/dx) = 8x-3y

Is this right so far? It doesn't seem like it's right because... well, how can you have an ln(dy/dx)??

Would you please help me with this part?
Thank you very much! :)

 

[Dick]

1. The next differential equation I'm working on is this:

dy/dx= e^{8x - 3y}

Alright, I thought to cancel out the e, we could take the ln of both sides...?

ln(dy/dx) = 8x-3y

Is this right so far? It doesn't seem like it's right because... well, how can you have an ln(dy/dx)??

Would you please help me with this part?
Thank you very much! :)

You can have ln(dy/dx) but there's not much you can do with it. Use e^(a+b)=e^a*e^b to separate the equation.

 

[rock.freak667]

This relationship will help a lot

e^a+b = e^a*e^b