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B. Applications from physics 3. Suppose a given spherical raindrop evaporates at the rate dV = -2V2/3 dt where V >0 is its volume, and the initial volume is V(0) = 8. (a) Sketch the graph of f(V) vs V. Draw the phaseline. (b) Find the solution V(t). Sketch the solution in the t-V plane. Is this solution consistent with your result in (a)?

B. Applications from physics 3. Suppose a given spherical raindrop evaporates at the rate dV = -2V2/3 dt where V >0 is its volume, and the initial volume is V(0) = 8. (a) Sketch the graph of f(V) vs V. Draw the phaseline. (b) Find the solution V(t). Sketch the solution in the t-V plane. Is this solution consistent with your result in (a)?

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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(c) At what time has the drop completely evaporated? (d) State two solutions to the differential equation that satisfy V(3) = 0. Show the graph of both solutions in your plot in (b). (e) You have clearly demonstrated non-uniqueness for the initial value problem in (d). Why does this not contradict theorem 2.4.2?
Transcribed Image Text:(c) At what time has the drop completely evaporated? (d) State two solutions to the differential equation that satisfy V(3) = 0. Show the graph of both solutions in your plot in (b). (e) You have clearly demonstrated non-uniqueness for the initial value problem in (d). Why does this not contradict theorem 2.4.2?
B. Applications from physics 3. Suppose a given spherical raindrop evaporates at the rate dV -2V2/3 dt where V > 0 is its volume, and the initial volume is V(0) = 8. (a) Sketch the graph of f(V) vs V. Draw the phaseline. (b) Find the solution V(t). Sketch the solution in the t-V plane. Is this solution consistent with your result in (a)?
Transcribed Image Text:B. Applications from physics 3. Suppose a given spherical raindrop evaporates at the rate dV -2V2/3 dt where V > 0 is its volume, and the initial volume is V(0) = 8. (a) Sketch the graph of f(V) vs V. Draw the phaseline. (b) Find the solution V(t). Sketch the solution in the t-V plane. Is this solution consistent with your result in (a)?
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