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dx As a salt dissolves in methanol, the number x(t) of grams of the salt in a solution after t seconds satisfies the differential equation = 1x-0.005x2. dt (a) What is the maximum amount of the salt that will ever dissolve in the methanol? (b) If x = 60 when t= 0, how long will it take for an additional 60 g of salt to dissolve?

dx As a salt dissolves in methanol, the number x(t) of grams of the salt in a solution after t seconds satisfies the differential equation = 1x-0.005x2. dt (a) What is the maximum amount of the salt that will ever dissolve in the methanol? (b) If x = 60 when t= 0, how long will it take for an additional 60 g of salt to dissolve?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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dx = 1x - 0.005x?. As a salt dissolves in methanol, the number x(t) of grams of the salt in a solution after t seconds satisfies the differential equation (a) What is the maximum amount of the salt that will ever dissolve in the methanol? (b) If x = 60 when t=0, how long will it take for an additional 60 g of sait to dissolve? (a) The maximum amount of the salt that will ever dissolve in the methanol is grams. (Simplify your answer.)
Transcribed Image Text:dx = 1x - 0.005x?. As a salt dissolves in methanol, the number x(t) of grams of the salt in a solution after t seconds satisfies the differential equation (a) What is the maximum amount of the salt that will ever dissolve in the methanol? (b) If x = 60 when t=0, how long will it take for an additional 60 g of sait to dissolve? (a) The maximum amount of the salt that will ever dissolve in the methanol is grams. (Simplify your answer.)
Expert Solution
Step 1

Properties of derivative 

ddxxn=nxn-1ddxcf(x)=cddxf(x)

Properties of integration 

∫1xdx=lnx∫af(x)dx=a∫f(x)dx

Second derivative test:

  1. Determine first derivative
  2. Find the critical point by equating derivative to zero
  3. Find the value of second derivative at the critical point then 
  • If second derivative is negative at the critical point then  maxima
  • If second derivative is positive at the critical point then minima
  • If second derivative is zero then it is point of inflection 

 

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