• Support PF! Buy your school textbooks, materials and every day products via PF Here!

Ordinary Differential Equation

1. The problem statement, all variables and given/known data
1. The problem statement, all variables and given/known data
Solve [tex] \frac{dz}{dt} + 3 t e^{t+z} = 0 [/tex]


2. Relevant equations
None that I can think of...


3. The attempt at a solution
"Rearranging" the given question, we get:

[tex] \int \frac{dz}{e^z} = -3\int t e^t dt [/tex]

[tex] -e^{-z} = -3 \left( t e^t - e^t \right) + C [/tex]
[tex] e^{-z} = 3 \left( t e^t - e^t \right) + C [/tex]
[tex] z = - ln \left( 3 t e^t - 3 e^t + C \right) [/tex]

Is this all correct? The system into which I need to enter this answer is saying im wrong :(
 

Ray Vickson

Science Advisor
Homework Helper
Dearly Missed
10,705
1,710
1. The problem statement, all variables and given/known data
1. The problem statement, all variables and given/known data
Solve [tex] \frac{dz}{dt} + 3 t e^{t+z} = 0 [/tex]


2. Relevant equations
None that I can think of...


3. The attempt at a solution
"Rearranging" the given question, we get:

[tex] \int \frac{dz}{e^z} = -3\int t e^t dt [/tex]

[tex] -e^{-z} = -3 \left( t e^t - e^t \right) + C [/tex]
[tex] e^{-z} = 3 \left( t e^t - e^t \right) + C [/tex]
[tex] z = - ln \left( 3 t e^t - 3 e^t + C \right) [/tex]

Is this all correct? The system into which I need to enter this answer is saying im wrong :(
Maybe it does not like the '-' sign; have you tried entering
[tex] \ln \left( \frac{1}{3 t e^t - 3 e^t + C}\right)?[/tex]
 
Maybe it does not like the '-' sign; have you tried entering
[tex] \ln \left( \frac{1}{3 t e^t - 3 e^t + C}\right)?[/tex]
Let's hope its that... I only get one more shot :(
 
I think you have to take the natural log of each part individually. [tex]lne^{-z}=ln3te^t-ln3e^t+lnc[/tex] that would give [tex]z=-ln3te^t+ln3e^t+lnc[/tex] Which simplifies to [tex]z=ln({\frac{c3e^t}{3te^t})}[/tex]
 

Ray Vickson

Science Advisor
Homework Helper
Dearly Missed
10,705
1,710
I think you have to take the natural log of each part individually. [tex]lne^{-z}=ln3te^t-ln3e^t+lnc[/tex] that would give [tex]z=-ln3te^t+ln3e^t+lnc[/tex] Which simplifies to [tex]z=ln({\frac{c3e^t}{3te^t})}[/tex]
No, you cannot do that. The answer I gave in my previous post was the one that Maple gave as the solution to the DE. The OP's workings were perfectly correct, as was the answer he gave.
 
No, you cannot do that. The answer I gave in my previous post was the one that Maple gave as the solution to the DE. The OP's workings were perfectly correct, as was the answer he gave.
Ah, apologies.
 

Want to reply to this thread?

"Ordinary Differential Equation" You must log in or register to reply here.

Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving
Top