Solve Calculus Question: dx/dt = -(2x)/(50+t)

[geowills]

What is dx/dt = -(2x)/(50+t) if you solve for x solely in terms of t? I tried to rearrange to make it separable but keep getting stuck.

 

[matt grime]

Homework questions are supposed to follow some guidelines: what have you done, give an example of your rearrangements that get stuck. That seems like an easy DE to solve since you can put the x's (and dx) on one side and the t's (and dt) on the other.

 

[aeroguy2008]

What is dx/dt = -(2x)/(50+t) if you solve for x solely in terms of t? I tried to rearrange to make it separable but keep getting stuck.

You did the same mistake I did when I started asking questions here and initially didn't show my attempt for a solution. As I did notice it myself later on...it actually helps if you show at least one of your attempts - even for self-reflection about the problem. Have you tried to cross-multiply?

 

[kreil]

Surely you know how to multiply, so obtaining this expression should be trivial:

$$\frac{dx}{dt} = - \frac{2x}{50+t} \implies \frac{dx}{2x}=- \frac{dt}{50+t}$$

Now, integrate both sides and then solve for x.