Test 3 _practice_ solutions

Test 3 _practice_ solutions - Math 1B Third Exam Name:_...

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Math 1B Third Exam Name:_________________________ SID:_____________________ (last, first) 1. The direction field for a differential equation is shown. a) Suppose (0) 0 y = . Using Euler’s method with a step-size of 1, what would the approximation for (2) y be? (7 points) (0) 1.5 y b) Would this be an underestimate or an overestimate? Explain your answer. (1 point) This is an underestimate. The slopes are increasing, so the function is concave up. c) Based on the picture above, is the differential equation autonomous? Justify your answer. (2 points) Yes, the equation is autonomous. For any fixed y -value, the slope is constant. It does not depend on x .
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2. a) Give an example of a first order differential equation that is separable but not linear. Solve your equation. 22 2 2 11 dy x ydy xdx y x C y x C dx y =→ = → = +→ − = b) Give an example of first order differential equation that is linear, but not separable. Solve your equation. () xxx x x xx x x dy yx dx dy dx dy ee y x e dx de y xe dx ey x e e C C e −−− −− =+→ −=→ =− + → =− + 3. You are thinking of buying a house and deciding whether you can afford to borrow $500,000. You can borrow the money at a 6% annual interest rate compounded continuously.
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Test 3 _practice_ solutions - Math 1B Third Exam Name:_...

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