# Differential equations problem (easy?)

• Jan 13th 2010, 09:52 AM
tom007
Differential equations problem (easy?)
do u know how to solve this : u'' + 1/r u' = 0 (i forgot the method and i don't have my notebook)
• Jan 13th 2010, 10:04 AM
Jhevon
Quote:

Originally Posted by tom007
do u know how to solve this : u'' + 1/r u' = 0 (i forgot the method and i don't have my notebook)

This is a Cauchy-Euler equation. Multiply through by $r^2$, to get $r^2u'' + ru' = 0$.

Now, go to Chris' differential equations tutorial (link in my signature) and see post #5
• Jan 13th 2010, 10:19 AM
DeMath
Quote:

Originally Posted by tom007
do u know how to solve this : u'' + 1/r u' = 0 (i forgot the method and i don't have my notebook)

Multiply by $r$

$u'' + \frac{u'}{r} = 0 \Leftrightarrow ru'' + u' = 0 \Leftrightarrow \left(ru'\right)^\prime = 0 \Rightarrow ru' = C_1 \Leftrightarrow u' = \frac{C_1}
{r} \Rightarrow u = C_1\ln|r| + C_2.$
• Jan 13th 2010, 10:22 AM
Jhevon
Quote:

Originally Posted by DeMath
Multiply by $r$

$u'' + \frac{u'}{r} = 0 \Leftrightarrow ru'' + u' = 0 \Leftrightarrow \left(ru'\right)^\prime = 0 \Rightarrow ru' = C_1 \Leftrightarrow u' = \frac{C_1}
{r} \Rightarrow u = C_1\ln|r| + C_2.$

even better! (Giggle)
• Jan 13th 2010, 10:24 AM
tom007
Quote:

Originally Posted by DeMath
Multiply by $r$

$u'' + \frac{u'}{r} = 0 \Leftrightarrow ru'' + u' = 0 \Leftrightarrow \left(ru'\right)^\prime = 0 \Rightarrow ru' = C_1 \Leftrightarrow u' = \frac{C_1}
{r} \Rightarrow u = C_1\ln|r| + C_2.$

yeea..now i remember!!! (Clapping) tnx!!!