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d²y (a) Solve the differential equation +y dx² y'(0) = 0. got up (4) pap = sin(x) + cos(x) with y(0) 1 and snop 1 p +90:09

d²y (a) Solve the differential equation +y dx² y'(0) = 0. got up (4) pap = sin(x) + cos(x) with y(0) 1 and snop 1 p +90:09

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.CR: Chapter 11 Review
Problem 33CR
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. (a) Solve the differential equation d²y dx² +y = sin(x) + cos(x) with y(0) = 1 and y'(0) = 0. (b) Consider an object of mass m, dropped from some initial height and falling down towards Earth's surface with velocity v(t) at time t. Suppose we choose to model the force of air resistance as being proportional to the square of the instantaneous speed. (i) If we choose "up" to be the positive y direction and set ß> 0 to be a con- stant of proportionality, briefly explain why the most appropriate differential equation to model this setup is dv = -mg+Bv² with v(0) = 0, dt rather than dv m- = -mg - Bv² with v(0) = 0. dt (ii) After setting m = 1, B 1, B = 10 and g = 10, solve this differential equation for the velocity of the object at time t. (iii) Determine the time at which the object reaches 90% of its terminal velocity. 3 (c) Evaluate √3x - x² dx. m-
Transcribed Image Text:. (a) Solve the differential equation d²y dx² +y = sin(x) + cos(x) with y(0) = 1 and y'(0) = 0. (b) Consider an object of mass m, dropped from some initial height and falling down towards Earth's surface with velocity v(t) at time t. Suppose we choose to model the force of air resistance as being proportional to the square of the instantaneous speed. (i) If we choose "up" to be the positive y direction and set ß> 0 to be a con- stant of proportionality, briefly explain why the most appropriate differential equation to model this setup is dv = -mg+Bv² with v(0) = 0, dt rather than dv m- = -mg - Bv² with v(0) = 0. dt (ii) After setting m = 1, B 1, B = 10 and g = 10, solve this differential equation for the velocity of the object at time t. (iii) Determine the time at which the object reaches 90% of its terminal velocity. 3 (c) Evaluate √3x - x² dx. m-
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