Hi all,

Thanks for helping me to solve the problem below using Maple.

dsys := {(1-4*(diff(ln(v(z)), z)))*(diff(u(z), z))+((3/2)*z^{-1}-2*(3* z^{-1} *(diff(ln(v(z)), z))+2*(diff(ln(v(z)),z,z )))))*u(z) = 0, -z*(diff(v(z), z))-v(z)+v(z)^(1/2)*u(z) = 0, v(0) = 1, u(0) = 1, (D(v))(0) = 1/4, (D(u))(0) = 3/8}

When trying sol := dsolve(dsys, numeric)

I got : Error, (in DEtools/convertsys) unable to convert to an explicit first-order system.

Note that the analytic solution for z<=0 is:

if z>-4 then u(z)=(1+z/4)exp(z/8) and v(z)=exp(z/4)

else u(z)=0 and v(z)= (-4/z)exp(-1)

Regards