My data has 150 samples and is not normally distributed, and it does not have equal variances either. I know t-test (e.g. this python method) can be used when data is normally distributed and it can be used when it does not have equal variance. So I am not sure if I can use the t-test when data is not normally distributed.
Alternatively, I thought, I should use a non-parametric test, e.g., the Mann-Whitney $U$ rank sum test, but as far as I know, the Mann-Whitney $U$ can be used only if the samples have equal variance!
My question is, am I correct, can't I use any of these test (t-test and Mann-Whitney $U$)? If not, which test should I use?