Solve the Bernoulli differential equation

[chwala]

Homework Statement

kindly look at the attachment below

Relevant Equations

Bernoulli

kindly note that my question or rather my only interest on this equation is how we arrive at the equation,

$v(x)=ce^{15x} - \frac {3}{17} e^{-2x}$ ...is there a mistake on the textbook here?

in my working i am finding,

$v(x)=-1.5e^{13x} +ke^{15x}$

 

[Frabjous]

Try plugging it into the differential equation and see if it is a solution.

 

[chwala]

Try plugging it into the differential equation and see if it is a solution.

I haven't talked about solution...my only interest is on the step of finding $v(x)$, is my $v(x)$ wrong?

 

[Frabjous]

There is an equation for v(x). Plug your v(x) into it.

 

[etotheipi]

I got the same as the book. Which is the first step in your solution that differs from the solution in the book?

 

[chwala]

ok this are my steps, let me know what i have done wrong...

 

[Frabjous]

The rhs is wrong.

 

[etotheipi]

ok this are my steps, let me know what i have done wrong...

It's just that after you found the integrating factor $\mu(x) = e^{-15x}$, you multiplied the LHS by it but forgot to also multiply the RHS by it! And so ended up with a false statement.

So just change the RHS to $3e^{-17x}$, and you should be good to go.

 

[chwala]

aaaaargh...i have seen it, i did not multiply both sides by integral factor.

 

[chwala]

 

[Frabjous]

aaaaargh...i have seen it, i did not multiply both sides by integral factor.

Not to be pedantic, but it is “integrating” factor.

May I make a general observation? I have seen several of your posts and you need to work on minimizing carelessness in your work. Some suggestions:
1) Slow down.
2) Don’t skip steps.
3) Look for ways to check your answers like I was suggesting above.
4) If you suspect your answer is wrong, and cannot find it or are doing correction after correction, start again with a clean sheet of paper and do not copy things. You will have learned stuff in the first attempt that will influence how you go at the problem a second time.
5) Be patient.

 

[chwala]

Not to be pedantic, but it is “integrating” factor.

May I make a general observation? I have seen several of your posts and you need to work on minimizing carelessness in your work. Some suggestions:
1) Slow down.
2) Don’t skip steps.
3) Look for ways to check your answers like I was suggesting above.
4) If you suspect your answer is wrong, and cannot find it or are doing correction after correction, start again with a clean sheet of paper and do not copy things. You will have learned stuff in the first attempt that will influence how you go at the problem a second time.
5) Be patient.

True caz, integrating factor it is...yeah I am always in a haste...Will slow down. Cheers

 

[Mark44]

3) Look for ways to check your answers like I was suggesting above.

Not to minimize the other steps that @caz mentioned, but the one here is very important.

 

[chwala]

Yeah true, by substituting $V(x)$ and its derivative...I should have checked if it satisfies the previous equation, specifically the exponential function on the right hand side.

 

[chwala]

I will just take time to re check my work before posting, I am refreshing on these areas as its long since I dealt with them. Definitely, I need to improve on 'silly' mistakes...but most importantly, what I am proud of is that I know and understand the concepts required. Bingo!

 

[chwala]

True caz, integrating factor it is...yeah I am always in a haste...Will slow down. Cheers

In other terms, it means that i should be able to solve the problems by myself with due diligence without necessarily running to the forum. Thats a compliment...I guess now, I will take time to ponder on problems than just rush as I have the capabilities...