# tioIn vvrunSecolld- order equations. 6. Use the method of Problem 5 to solve the equation 1. nditions. of the dy dt ayb. 7. The field mouse population in Example 1 satisfies the differential equation dyP 450. dt 2 a. Find the time at which the population becomes extinct if p(O) 850. b. Find the time of extinction if p(0) Po, where 0< po< 900 N c. Find the initial population po if the population is to become extinct in 1 year e same. om the fied by 8. The falling object in Example 2 satisfies the initial value to solve problem dv 9.8 v0) 0 dt (31) a. Find the time that must elapse for the object to reach 98% of its limiting velocity. h How far does the object fall in the time found in part a? (221

Question

Given the equation dy/dt=(p/2)-450
Find the time of extinction if p(0)=psub0, where 0

This is question number 7

Step 1

As per the given information, it seems that there is a typing error in the question. According to Leibnitze linear equation, instead of dy/dt, it should be dp/dt.

So, I will be solving the question considering the equation to be : dp/dt = p/2 - 450.

According to Leibnitze linear equation, the standard form of an ODE is :    dp/dt + Ry = S, where R, S are arbitary functions of t.

The general solution of this ODE is: p(t) x I.F = ∫S(I.F) dt +C, where Integrating Factor, I.F = e∫Rdt.

Now, let us solve the given ODE accordingly:

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