For 'biochemistry' grasp of linear ode's with constant coefficients will see you through. A good grasp of that - matrix formulation, eigenvalues, eigenvectors which it does not take all that long to master will be an advantage. (Linearisation of nonlinear equations for local analysis which gives good idea of overall behaviours of unsolvable equations is then a fairly obvious application you might meet in the biomath reaches.) Being not thrown by matrices and a bit handy with them is good to have because in the systems you deal with not just one thing is happening at a time. Applications in kinetics and related rather physical biochemistry. That and any bit more does no harm for physical methods used in biochemistry.
But if you've got that much you'll be considered "the mathematician" among biochemists. Your classmates will be guys who are thrown by "v = s/(K + s) , then s = what? in terms of v and K". A few years ago at school they could do it when it was Exercise 3 of Chapter 5 math. But no one gave them the idea it would ever be used for anything or could mean anything outside Chapter 5. They might just still manage by dint of memory y = x/(K + x) but not v = s/(K + s)!
I'll always remember the words of one old biochem Prof. "Ah all right for you, you're a mathematician." I said Me!? I am not a mathematician by any stretch. "OK" he said "But you're not frightened of it, that's the big point"
Non-linear d.e.'s and pde's is pretty much outside 'biochemistry' and mol. biol. and a specialist area for evolutionary theory, 'biomath' modelling etc. There is plenty of help available for biochemists who do want to get into such areas. These areas are almost not a 'subject', more of a hotch-potch. I agree with snipez. lde's can't be escaped and shouldn't try - needed for even the background physics minimum.
More generally every kind of biologist now has to be quite interdisciplinary so learning of math is not really wasted. Beyond a certain point though a biochemist has to learn biochemistry!