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Differential Equation

Off-diagonal
in Analysis and Calculus

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[math] \frac{H''}{H}+\frac{2}{r}\frac{H'}{H} = 0 [/math]

 

 

when H is a function of r and H" is second derivative with respect to r

solve for H

 

please help me

A first obvious step is to multiply through by H!

 

You now have [math]H"+ \frac{1}{r}H'= 0[/math]. Let Y= H' and now

[math]Y'+ \frac{1}{r}Y= 0[/math] or [math]Y'= -\frac{1}{r}Y[/math] which is a simple separable equation. Solve for Y, then solve H'= Y. Remember that the solution is only valid for H not equal to 0.

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