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Help with Differential Equations please!

  • Thread starter Jay9313
  • Start date
1. The problem statement, all variables and given/known data
[itex]\frac{dy}{dx}[/itex]=3y f(2)=-1
and
[itex]\frac{dy}{dx}[/itex]=e[itex]^{y}[/itex]x when x=-2 y=-ln(3)
I'm in Calc AB By the way, so please do not try to show me methods that are too advanced.
2. Relevant equations
There are no relevant equations?


3. The attempt at a solution
My attempt at the first solution is
[itex]\int[/itex][itex]\frac{dy}{3y}[/itex]=[itex]\int[/itex]dx
[itex]\frac{ln(y)}{3}[/itex]=x+c
y=e[itex]^{3x+3c}[/itex]
ln(-1)=6+3c
You can't have that Natural Log though.. So I 'm stuck.

My attempt at the second solution is..
∫[itex]\frac{dy}{e^{y}}[/itex]=∫x dx
-[itex]\frac{1}{e^{y}}[/itex]=[itex]\frac{x^{2}}{2}[/itex]+c
-ln(e[itex]^{-y}[/itex])=e[itex]^{}\frac{x^{2}+2c}{2}[/itex]
-ln(3)=e[itex]^{}\frac{4+2c}{2}[/itex]
 
Last edited:

HallsofIvy

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1. The problem statement, all variables and given/known data
[itex]\frac{dy}{dx}[/itex]=3y f(2)=-1
and
[itex]\frac{dy}{dx}[/itex]=e[itex]^{y}[/itex]x when x=-2 y=-ln(3)
I'm in Calc AB By the way, so please do not try to show me methods that are too advanced.
2. Relevant equations
There are no relevant equations?


3. The attempt at a solution
My attempt at the first solution is
[itex]\int[/itex][itex]\frac{dy}{3y}[/itex]=[itex]\int[/itex]dx
[itex]\frac{ln(y)}{3}[/itex]=x+c
Your integration has a common mistake. The integral of 1/y is NOT ln(y), it is ln(|y|).

y=e[itex]^{3x+3c}[/itex]
ln(-1)=6+3c
You can't have that Natural Log though.. So I 'm stuck.
(I'm going to submit this and go back and show my solution for the second one since it takes me a little while to put this in.)
(2) is also easy to integrate.
 
Oh man, I'm so used to the absolute value not mattering,that it screwed me up =/ Thank you soooo much.
 

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