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4. Suppose that a body moves through a resisting medium with resistance proportional to its velocity v, so that dv/dt = -kv. a. Show that its velocity and position at time t are given by and v(t)= voe -kt x(t) = x + (%) (1 − e¯kt). b. Conclude that the body travels only a finite distance, and find that distance.

4. Suppose that a body moves through a resisting medium with resistance proportional to its velocity v, so that dv/dt = -kv. a. Show that its velocity and position at time t are given by and v(t)= voe -kt x(t) = x + (%) (1 − e¯kt). b. Conclude that the body travels only a finite distance, and find that distance.

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter11: Differential Equations
Section11.3: Euler's Method
Problem 1YT: Use Eulers method to approximate the solution of dydtx2y2=1, with y(0)=2, for [0,1]. Use h=0.2.
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c. r² tan(y)y' + tan(y)y' 4. Suppose that a body moves through a resisting medium with resistance proportional to its velocity v, so that dv/dt = -kv. a. Show that its velocity and position at time t are given by v(t) = voe and = -kt x(t) = x + ( ) (1 − e¯kt). VO k b. Conclude that the body travels only a finite distance, and find that distance. 5. Determine whether or not the initial value problem dy dx has a solution. Is the solution unique? 6. Determine whether or not the initial value problem dy Vy; y(0) = 0 dx has a solution. Is the solution unique? √xy; y(2) = 1
Transcribed Image Text:c. r² tan(y)y' + tan(y)y' 4. Suppose that a body moves through a resisting medium with resistance proportional to its velocity v, so that dv/dt = -kv. a. Show that its velocity and position at time t are given by v(t) = voe and = -kt x(t) = x + ( ) (1 − e¯kt). VO k b. Conclude that the body travels only a finite distance, and find that distance. 5. Determine whether or not the initial value problem dy dx has a solution. Is the solution unique? 6. Determine whether or not the initial value problem dy Vy; y(0) = 0 dx has a solution. Is the solution unique? √xy; y(2) = 1
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