Are SI Units Equivalent in Differential Equations?

[mlsbbe]

Hi all,
I would like to know if any of you know about anything the equivalence of SI units for differential equations? For example, for the equation

E=mc² SI units for RHS must equal LHS. I am wondering if this would apply to differential equations?

I recently came across a journal paper with the following forumula:

$$\frac{dP}{dx}=\beta P+C$$

Where $$\beta$$, $$C$$, is a constant. $$x$$ is the length in metres

Now, P equals to the power (in W). In this case, can you evaluate both RHS and LHS in terms of SI units? It seems to me that both the LHS and RHS of this equation is not equivalent.

 

[rock.freak667]

dP/dx can be approximated to ΔP/Δx to give units of Wm^-1

 

[diazona]

Hi all,
I would like to know if any of you know about anything the equivalence of SI units for differential equations? For example, for the equation

E=mc² SI units for RHS must equal LHS. I am wondering if this would apply to differential equations?

Yep, it applies to all equations. Both sides, and all terms, have to have the same units, otherwise it's not a physically meaningful equation. Note that in some unit systems, certain constants may have a numerical value of 1 and are conventionally omitted - for example, in natural units you can write $E = m$ - but when you switch to another unit system (like SI) in which the constants are not "trivially valued" you need to put them back in.

In
$$\frac{dP}{dx}=\beta P+C$$
using SI units, the constant $\beta$ has to have units of $\mathrm{m}^{-1}$ and $C$ has to have units of $\mathrm{W/m}$.

 

[berkeman]

Hi all,
I would like to know if any of you know about anything the equivalence of SI units for differential equations? For example, for the equation

E=mc² SI units for RHS must equal LHS. I am wondering if this would apply to differential equations?

I recently came across a journal paper with the following forumula:

$$\frac{dP}{dx}=\beta P+C$$

Where $$\beta$$, $$C$$, is a constant. $$x$$ is the length in metres

Now, P equals to the power (in W). In this case, can you evaluate both RHS and LHS in terms of SI units? It seems to me that both the LHS and RHS of this equation is not equivalent.

The units have to match on the LHS and RHS. So the units of Beta must be 1/m, and the units of C must be W/m.

 

[mlsbbe]

Thanks for your reply guys.

I was confused because the constant C is called the spontaneous emission power, which is confusing since power is measured in watts.

 

[berkeman]

Thanks for your reply guys.

I was confused because the constant C is called the spontaneous emission power, which is confusing since power is measured in watts.

Sounds like a good time to gently point out their error to them.