Differential equations problem (easy?)

**tom007** · January 13th 2010, 09:52 AM

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

**Jhevon** · January 13th 2010, 10:04 AM

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

**DeMath** · January 13th 2010, 10:19 AM

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 $r$

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

**Jhevon** · January 13th 2010, 10:22 AM

Originally Posted by DeMath

Multiply by $r$

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

even better!

**tom007** · January 13th 2010, 10:24 AM

Originally Posted by DeMath

Multiply by $r$

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

yeea..now i remember!!!

tnx!!!

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