- #1
Suicidal
- 22
- 1
In my calculus course I was tough to solve differential equations by separation and then integrating
For instance
dv/dt = a
dv = a*dt
v= a*t + c (c is a constant of integration)
then if I was given an initial condition such as v(0)=Vo I would substitute into my general solution
and get
Vo=a*0+c=c
V=a*t+Vo
Now that I started learning physics I keep coming across this funny way of solving differential equations:
v
[inte] dv=
Vo
t
[inte] a*dt
0
Why does this second method work. I realize that it is probably somehow equivalent to the first I just don’t see it. I would really like to know how and why this second method works.
For instance
dv/dt = a
dv = a*dt
v= a*t + c (c is a constant of integration)
then if I was given an initial condition such as v(0)=Vo I would substitute into my general solution
and get
Vo=a*0+c=c
V=a*t+Vo
Now that I started learning physics I keep coming across this funny way of solving differential equations:
v
[inte] dv=
Vo
t
[inte] a*dt
0
Why does this second method work. I realize that it is probably somehow equivalent to the first I just don’t see it. I would really like to know how and why this second method works.