Initial volume is 5cm^3 and an hour later it becomes half of the initial. t is hours (initially t=0) Solve for particular solution of differential equation as well as find how long does it take for V=0 surface area: S=kV^2/3 Differential equation: dV/dt= kV^2/3 General solution: V=(1/3kt+c)^3
Initial volume is 5cm^3 and an hour later it becomes half of the initial. t is hours (initially t=0) Solve for particular solution of differential equation as well as find how long does it take for V=0 surface area: S=kV^2/3 Differential equation: dV/dt= kV^2/3 General solution: V=(1/3kt+c)^3
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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Initial volume is 5cm^3 and an hour later it becomes half of the initial.
t is hours (initially t=0)
Solve for particular solution of differential equation as well as find how long does it take for V=0
surface area: S=kV^2/3
Differential equation: dV/dt= kV^2/3
General solution: V=(1/3kt+c)^3
Expert Solution
Step 1
Given the differential equation
Step 2
Integrate both sides
Step 3
Now, find the initial conditions.
Step 4
Substitute the initial conditions and find the constants.
First, put V(0) = 5 to get
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