i've derived the following differential eqn from a problem i'm working on, and i have tried in vain to solve this if any one can give a direction where i should go our how to attack would be greatly appreciated. the eqn is(adsbygoogle = window.adsbygoogle || []).push({});

[tex]I\,r= -L\dot{I}+\frac{3}{2}\mu_{0}m R^{2}\frac{z \dot{z}}{\left(R^{2}+z^{2}\right)^{5/2}} [/tex]

where [tex] r,L,m,\mu_{0},R,\dot{z} [/tex] are all constants. one of two ways i've tried solving this, was since

[tex]\dot{z}=const.\Rightarrow z=\dot{z}t [/tex]

which just gives a particular solution i cannot find a solution for. the homogeneous part is quite trivial with the solution being

[tex] I_{homogeneous}=const. \, \exp(-rt/L)[/tex]

am i missing something, is there another way. any help please

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# Homework Help: First order differential equation help

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