Getting 0 for a particular solution: r^2*dy/dr = K, r>0, K constant

bulldog160

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I have this question that I am struggling to see if it is correct or not.

A quantity y(r) satisfies the first-order fifferential equation r^2*dy/dr = K where r > 0 and K is a constant.

The general solution I got from this FO differential equation is: y = K(-1/r + F)


The second part to this question is to find a particular solution for y(R) = 0, where R is a constant.

I seem to get 0 as R = 1/F which cancels out everything.


Much appreciated for anyone that can help.
 
Okay, that's fine, but:

1) There is no need to produce TWO constants of integration. One will do.
2) Is K(Ar + B) really different from KAr + KB? KB is still just come constant of itegration.
3) You are VERY close.

We'll do it your way.

\(\displaystyle K\cdot\left(-\dfrac{1}{R}+F\right)=0\) has two solutions. One of those is K = 0. You are not interested in this solution. The other solution is F = 1/R.

You are done. What is this cancelling out of which you speak?

Substitute: \(\displaystyle Y(r) = K\cdot\left(-\dfrac{1}{r} + \dfrac{1}{R}\right)\) -- Perhaps you are confusing "R" with "r"?
 
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Okay, that's fine, but:

1) There is no need to produce TWO constants of integration. One will do.
2) Is K(Ar + B) really different from KAr + KB? KB is still just come constant of itegration.
3) You are VERY close.

We'll do it your way.

\(\displaystyle K\cdot\left(-\dfrac{1}{R}+F\right)=0\) has two solutions. One of those is K = 0. You are not interested in this solution. Please find the other solution.

OK.

-1/R + F = 0

You are left with R = 1/F. Yet, if we subsitute this back into the general solution, we get K*0, as the two F's cancel each other out.
 
Okay, that's fine, but:

1) There is no need to produce TWO constants of integration. One will do.
2) Is K(Ar + B) really different from KAr + KB? KB is still just come constant of itegration.
3) You are VERY close.

We'll do it your way.

\(\displaystyle K\cdot\left(-\dfrac{1}{R}+F\right)=0\) has two solutions. One of those is K = 0. You are not interested in this solution. The other solution is F = 1/R.

You are done. What is this cancelling out of which you speak?

Substitute: \(\displaystyle Y(r) = K\cdot\left(-\dfrac{1}{r} + \dfrac{1}{R}\right)\) -- Perhaps you are confusing "R" with "r"?

You're right. I am confusing "r" with "R".

Shouldn't the answer be y(r) = K(-1/r + 1/R) ? <== Good catch! Typos have been repaired, above..
 
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