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A math worksheet focusing on solving differential equations and initial value problems. Topics include finding explicit solutions, equilibrium solutions, and graphing slope fields. It also includes a problem related to population growth and cooling rates.
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MATH 225 To get full credit, you must show all of your work. – Worksheet #2 Name:________________________________ Sec:________
dy dt = (^3) y + t t (^2) y , y " 0
c. Now assume that a the bacteria is being killed by the poison is poison is dropped into the Petri dish. The rate at which !
equation from part (a) to take into account this new factor, but do not solve this new ODE. Is this equation linear?^ .001 P^2. Change the differential d. For each ODE from parts (a) and part (c), find all the equilibrium solutions, in other words when !
answer in terms of the growth constant, k.^^ dP^ dt^ =^0. When applicable leave your
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dy dt = t (^2) " y ________ b. !
dy dt = sin( y ) ________ c. !
dy dt = sin( t ) ________ d. !
dy dt = y (^2) " t ________ I. II.
