- #1
xman
- 93
- 0
i've derived the following differential eqn from a problem I'm working on, and i have tried in vain to solve this if anyone can give a direction where i should go our how to attack would be greatly appreciated. the eqn is
[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
[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