- #1
LENIN
- 102
- 1
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 experience with differential equations (they are not in our high school 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 can't integrate v by dt becouse t is not a veriable in v and v is therefore 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.
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 can't integrate v by dt becouse t is not a veriable in v and v is therefore 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.