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### Course: AP®︎/College Calculus AB>Unit 9

Lesson 1: AP Calculus AB 2017 free response

# 2017 AP Calculus AB/BC 4c

Potato problem from 2017 AP exam (Question 4, part c). Finding a particular solution for a separable differential equation.

## Want to join the conversation?

• where is the C for the integral with (G-27)^(-2/3)?
• The constants of integration are entirely arbitrary, so we don't need one on each side.

Let's, for argument's sake, have one on both sides ie
3(G - 27)^(1/3) + C₁ = -t + C₂
We could take C₁ from both sides:
3(G - 27)^(1/3) = -t + C₂ - C₁
But since they are arbitrary we can let C = C₂ - C₁ and so we have
3(G - 27)^(1/3) = -t + C
• What if the negative sign on (G-27) was not transferred to t? Wouldn't the constant be negative 12 instead? How did Sal know to move the negative over with the t?
• It doesn't matter. He could have moved it before, during, or after integration; G(t) would still be the same in all cases.
• i don't understand it when sai says"we were not only able to solve for the general solution. We were able to find the particular solution using this initial condition right here the G of zero is equal to 91."at
• Sal finishes solving for the general solution at ; this is the equation for G that solves the given differential equation. With the general solution, C could equal any constant, and the equation would still hold true. However, Sal is also given the initial condition of G(0) = 91, which limits C to one single value, making G a particular solution. Hope that I helped.
• Did you solve this from material learned from differential equations? I'm studying for an upcoming integrals test and this seemed confusing. So hopefully I shouldn't have to know this right now.
• At , how did Sal turn `dG/((G-27)^2/3)` into `(G-27)^2/3 dG` ?