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Calculus
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13 Nov 2019

1.Solve the problem. Find the demand function q = D(x), given that E(x) = 8/x and q = e when x=8 a) q = e^8/x b) q = ln 8/x c) q = 8 lnx d) q = ln^8/x

2. Solve 3y^2 dy/dx = 7x a) y = - 3sqrt(7/2 x^2 +C) b) y = - 3sqrt(7x +C) c) y = 3sqrt(7x^2 +C) d) y = 3sqrt(7/2 x^2 +C)

3. Find the general solution for the differential equation.
y ' = 72x^2 - 20x a) 72x^3 - 20x^2 + C b) 72x^3 - 10x^2 + C c) 24x^3 -10x^2 + C d) 24x^3 - 20x^2 + C


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Tod Thiel
Tod ThielLv2
4 Sep 2019

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Related questions

1. Find the general solution of the differential equation, or the particular solution if an initial condition is given.
xy' + 7y = x^2; y(2) = 12 a) y = x^2/9 + 13,312/9x^7 b) y = x^2/9 + 10,113/9x^7 c) y = x/9 + 13,312/9x^7 d) y = x^2/9 + 10,113/9x^9

2. Solve the differential equation model of radioactive decay: dQ/dt = -0.2Q.

a) Q(t) = -1/0.2t +Q b) Q(t) = Q e^-t c) Q(t) = -Q ln 0.2t + c d) Q(t) = Q e^-0.2t1.


Follow the six steps below to solve the following: xy' + 6xy =xe^(5x)


Step 1: REWRITE into standard form (y' + P(x)y + Q(x))



a) How does the given equation differ from standard form?



b) What can be done to put the given equation into standardform?





Step 2: IDENTIFY P(x) and Q(x).


a) Where does the standard form indicate P(x) and Q(x) arelocated?

P(x) =

Q(x) =





Step 3: DETERMINE the integrating factor (e^(?P(x) dx)). PlugP(x) as identified in step 2 into the integrating factor forme^(?P(x) dx) . Hint: Simplify e^(?P(x) dx) if possible




a) What is meant by the integrating factor?




b) If the integrating factor looks like e^(ln (x)) how could itbe simplified?





c) What about e^(1/2 ln (x))?





d) What about e^(-ln (x))?






?P(x) dx =




e^(?P(x) dx) =





Step 4: SUBSTITUTE Q(x) from step 2 and e^(?P(x) dx) from step 3into the solution form ye^(?P(x) dx) = ?Q(x)e^(?P(x) dx) + C.






Step 5: INTEGRATE the right side of the result of step 4. Hint:You may need to simplify and/or rewrite the right side before youattempt to integrate.






Step 6: SOLVE for y. To do this divide both sides by theintegrating factor. Remember that all parts of the right sideincluding the C must be divided by the integrating factor.






Solution is _________________________

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