I found this exercise in an old physics schoolbook. I maeged to solve it but I don't really understand why I have to solve it in this excact order. Before I start I would just like to add that I have very little experiance with differential equations (they are not in our highschool year plan), and therefor any explanations will be welcomed. So here it goes. t=? s=10 v=2s+1 v=ds/dt dt=(1/v)ds t=Iteg[1/v]ds t=1/2Ln(2s+1) This is the way it was solved in the book (I might have memorized the integration of v wrong). But I tried to solve it like this t=? s=10 v=2s+1 v=ds/dt ds=v*dt s=(2s+1)t s/(2s+1)=t The solutions are clearly different. I don't understend why. The only idea I got was that I cant integrate v by dt becouse t is not a veriable in v and v is therfore threted as a constent what changes the whole thing (is this true). But if there are any beter explanations I would be glad to hear them. Thanks.