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2051C06T1

# 2051C06T1 - If no Why If yes solve it c(10 Let y(0)=2 and...

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1 Prof. Tang MA2051 C06 Test 1 Section______ Name:_________________________ Problem 1 2 3 4 Total Possible Points 25 25 25 25 100 Points awarded Write Clearly, Show Your Work 1. (25%) Solve: dy/dx + (2sinx) y = sin x, y(0)=8 by using variation of parameters method.

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2 2. (25%) Solve: du/dt + 2 u = e – 2 t + 3 where u = u(t).
3 3. Let dy/dx = 2x y 2 . a) (5%) Is this equation linear? Why? b) (10%) Can it be solved by separation of variables?
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Unformatted text preview: If no, Why? If yes, solve it. c) (10%) Let y(0)=2 and ∆ x=0.25. Use Euler's method to find y(0.5). 4. A heat-loss model is given by dT/dt = -2 (T-4). a) (10%) Find the general solution; b) (7%) Find the steady state solution if any; c) (8%) Is the steady state solution stable or unstable? Justify your answer (phaseline or limit methods are both fine)....
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