a) Air Resistance, the differential equation describing the velocity, v of a falling mass m, subject to airresistance proportional to the instantaneous velocity is:dv(t)= mg - kv(t)dtwhere k> 0 is a constant of proportionality and g is the gravitational constant. The positive direction isdownward. Solve the equation subject to the initial condition v(0) = vo (Hint: m and vo are also constants).Solve the above problem through the following steps:1. Place the linear ODE in its standard form.2. Calculate the integration factor.3.Multiply the standard form of the equation by the integration factor.4. LHS of the resulting equation produced in point 3 above, is the derivative of the integrating factor and y.Integrate both sides of the resulting equation produced in point 4 above5.6.Write down the solution of ODE.m7. Apply initial condition (IC) to the solution above and solve for constant "C".8. Write down the final solution of the ODE.

Air Resistance, the differential equation describing the velocity, v of a falling mass m, subject to air resistance proportional to the instantaneous velocity is: dv(t) = mg - kv(t) dt where k> 0 is a constant of proportionality and g is the gravitational constant. The positive direction is downward. Solve the equation subject to the initial condition v(0) = vo (Hint: m and vo are also constants). Solve the above problem through the following steps: m 1. Place the linear ODE in its standard form. 2. Calculate the integration factor. 3. Multiply the standard form of the equation by the integration factor. 4. LHS of the resulting equation produced in point 3 above, is the derivative of the integrating factor and y. 5. Integrate both sides of the resulting equation produced in point 4 above 6. Write down the solution of ODE. 7. Apply initial condition (IC) to the solution above and solve for constant "C". 8. Write down the final solution of the ODE.

Air Resistance, the differential equation describing the velocity, v of a falling mass m, subject to air resistance proportional to the instantaneous velocity is: dv(t) = mg - kv(t) dt where k> 0 is a constant of proportionality and g is the gravitational constant. The positive direction is downward. Solve the equation subject to the initial condition v(0) = vo (Hint: m and vo are also constants). Solve the above problem through the following steps: m 1. Place the linear ODE in its standard form. 2. Calculate the integration factor. 3. Multiply the standard form of the equation by the integration factor. 4. LHS of the resulting equation produced in point 3 above, is the derivative of the integrating factor and y. 5. Integrate both sides of the resulting equation produced in point 4 above 6. Write down the solution of ODE. 7. Apply initial condition (IC) to the solution above and solve for constant "C". 8. Write down the final solution of the ODE.

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

Section11.1: Solutions Of Elementary And Separable Differential Equations

Problem 54E: Plant Growth Researchers have found that the probability P that a plant will grow to radius R can be...

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