1). The general solution of xdy/dx ? 3y = x^3y^1/3 is: (a) y1/3 = 2x3 + Cx2 (b)
ID: 3140723 • Letter: 1
Question
1). The general solution of xdy/dx ? 3y = x^3y^1/3 is:(a) y1/3 = 2x3 + Cx2
(b) y2/3 = 23x3 + Cx2
(c) y2/3 = 23x2 + Cx2
(d) y = 23x3 + Cx?2
(e) None of the above.
2). The general solution of yy^1 = xe^x2+y2
is:
(a) y2 = ln _ 1C ? ex2
(b) y2 = pC ? ex2
(c) y2 =xC + ex2
(d) y = ln(C ? ex2)
(e) None of the above.
3). The family of orthogonal trajectories of the family y^2 = Cx^3? 1 is:
(a) x2? 3y2 + 2 ln y = C
(b) 3y2? 2x2 + 3 ln y = C
(c) 2x2 + 3y2 + 6 ln y = C
(d) 3 ln y ? 2x2? y2 = C
(e) None of the above.
4). The family of orthogonal trajectories of the family of circles with center at the point (2,3)
is:
(a) y ? 3 =C/x ? 2
(b) y = ln(x ? 2) + C
(c) (y ? 3) = C(x ? 2)2
(d) y ? 3 = C(x ? 2)
(e) None of the above.
5). If $100 is deposited in a bank that pays 6% interest compounded continuously, then the amount in the account at the end of 5 years is (Hint: The population growth law applies.)
(a) $134.99
(b) $152.67
(c) $148.43
(d) $131.22
(e) None of the above.
6). Two years ago a laboratory had 100 grams of a certain radioactive material. Now it has 80 grams. How much will the laboratory have 3 years from now?
(a) 53.21 grams
(b) 71.55 grams
(c) 66.47 grams
(d) 57.24 grams
(e) None of the above.
7). Scientists observed that a small colony of penguins on a remote Antarctic island obeys the
population growth law. There were 2000 penguins initially and 3000 penguins 18 months
later. How long will it take for the number of penguins to double?
(a) 4.11 years
(b) 3.24 years
(c) 2.56 years
(d) 2.07 years
(e) None of the above.
8). What is the half-life of a radioactive material if it takes 5 hours for 1/3 of the material to
decay?
(a) 11.26 hours
(b) 8.55 hours
(c) 7.84 hours
(d) 10.21 hours
(e) None of the above.
9). At 12 noon on Sept. 12, the count in a bacteria culture was 400; at 4:00 pm the count was
1200. Let P(t) denote the bacteria count at time t and assume that the culture obeys
the population growth law. What was the bacteria count at 10 am on Sept. 12?
(a) 198
(b) 231
(c) 259
(d) 214
(e) None of the above.
Explanation / Answer
So that, the general solution: y = [2.x^3/3 + C.x^2]^(3/2)
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