# Mechanics, rewrite and solve equation, change of variables.

1. Aug 20, 2013

### fed_ex

Equation found in previous question is #: x''=gsin(a)-b(v^2)
1. Rewrite the equation # as a differential equation for v as a function of x.
2. Solve the equation to find v as a function of x.

Relevant equations: v=x'=dx/dt, x''=v'=a=dv/dt

Attempt at 1: Using the relevant equations you can rewrite # as
*: dv/dt=gsin(a) - b((x')^2)
Which i am scepticle of being correct due to my inability to solve it in the 2nd part.
Attempts at 2:Tried integrating but the whole((x')^2) confused me, i was thinking of making that (dx/dt)*(dx/dt) but got stuck again.
Tried to rewrite * but i was expecting a first order LINEAR equation, so that i could use the integrating factor method, so alas that also didn't work.

Any help would be appreciated, thankyou.

2. Aug 20, 2013

### tiny-tim

hi fed_ex! welcome to pf!

(try using the X2 button just above the Reply box )
correct, but you've gone a bit too far …

try dv/dt=gsin(a) - b(v2)

3. Aug 20, 2013

### HallsofIvy

Staff Emeritus
You are asked to find a differential equation for v as a function of x so you want derivatives with respect to x, not t.
By the chain rule, x''= dv/dt= (dv/dx)(dx/dt)= v (dv/dx).

Replacing x'' in the equation by v (dv/dx) gives the equation you want.

4. Aug 21, 2013

### fed_ex

Ah yes! Then separate and enjoy tasty solution.
Thanks!

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