Math 4B Midterm Exam

5 points consider the initial value problem jj j 9

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(5 points) Consider the initial value problem: JJ\ j (9 t2)y' + 2ty = ln(< + 5), Determine (without solving the problem) the largest interval in which the solution of this IVP is certain to exist. /* (J_ 4 Q / vÿFT A 3d v C (Cÿ [-W 0(S. 0ÿ 1 -7- / V 2. (5 points) A tank initially contains 15 lbs of salt dissolved in 150 gallons of water. Then water containing 4 lbs of salt per gallon is poured into the tank at a rate of 3 gallons per minute, and the well-stirred mixture is allowed to leave the tank at the same rate. Let Q{t) be the amount of salt at t minutes after this process started. Set up (but don’t solve) an initial value problem that describes this situation (i.e., write down a differential equation and initial condition). ivf- jj & -Ai >'* /7 V «rW- 1 m--* I -I fr\U 0Cÿ fM. \ *

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(0 Vr- Zh y-- t(zÿ2/vT 3. (10 points) (a) Find the solution of the initial value problem V? y{1)=2 y Y - il Y 0ÿ m v in explicit form. fro it t) (TTFT. t o\ y V 2. 't - i - ? - 1- k 'X»n«A. ,f 'I* ()<* ~L - 0 -V C --T, c (b) Determine the interval in which the solution is defined. 4 4- - K ~1 - xCh) ri< =- <? f T. “0 -'ÿf - ( f-*'V£t¥s> f\r** ~L -It S7 -ia -vÿ tv 1 Sollÿ TK> W>
) 4.

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