how do I manipulate r(dv_theta/dr)+v_theta = c_1 r into d(rv_theta)/dr = c_1 r?

[shreddinglicks]

This is part of a derivation involving the Navier-Stokes equation for fluid mechanics.

How does this:

. . . . .\(\displaystyle r\, \dfrac{dv_{\theta}}{dr}\, +\, v_{\theta}\, =\, c_1\, r\)

become this:

. . . . .\(\displaystyle \dfrac{d\, (r v_{\theta})}{dr}\, =\, c_1\, r\)

How do I manipulate the problem?

 

[Ishuda]

This is part of a derivation involving the Navier-Stokes equation for fluid mechanics.

How does this:

. . . . .\(\displaystyle r\, \dfrac{dv_{\theta}}{dr}\, +\, v_{\theta}\, =\, c_1\, r\)

become this:

. . . . .\(\displaystyle \dfrac{d\, (r v_{\theta})}{dr}\, =\, c_1\, r\)

How do I manipulate the problem?

Use the product rule for d(r v\(\displaystyle _\theta\))/dr

 

[shreddinglicks]

Use the product rule for d(r v\(\displaystyle _\theta\))/dr

If I try the product rule, how does that eliminate my V theta term?