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Quiz-6 / Re: Q6 TUT 0101
« on: November 18, 2018, 12:57:01 PM »
My answer is different.
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Quiz-6 / Re: Q6 TUT 0401
« on: November 18, 2018, 12:50:58 PM »
My answer to c is slightly different.
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MAT244--Lectures & Home Assignments / Re: quiz 5 0701
« on: November 06, 2018, 11:48:25 PM »
Can you show me the detailed integral of y2?
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MAT244--Lectures & Home Assignments / quiz 5 0701
« on: November 06, 2018, 10:07:24 PM »
Can anyone explain the integral here? I tried by parts but don't know how.
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MAT244--Lectures & Home Assignments / section 4.4
« on: November 01, 2018, 11:43:12 PM »
What's the strategy to choose from using the undetermined coefficient method or variation of parameters method?
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MAT244--Lectures & Home Assignments / sketch a graph
« on: November 01, 2018, 11:40:54 PM »
What's the strategy to sketch a graph of the solution in the x1- x2 plane for t>0?
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Quiz-4 / Re: Q4 TUT 0601
« on: October 26, 2018, 09:49:14 PM »
For the homogeneous equation,
r² + 1 = 0
r = i or −i
So, the complementary solution is y = C1cost + C2sint
W[y1,y2] =y1y2' − y1'y2 = cos²t + sin²t = 1
u1(x)=−∫(y2(x)g(x)/W)dx
= −∫(sint tant) dt
= sint − ln(tant+sect)
u2(x)=∫(y1(x)g(x)/W)dx
= ∫(cost tant)dt
= ∫sint dt
= −cos t
So, a particualr solution is
y = u1y1+u2y2
=[sint - ln(tant+sect)]cost − costsint
=−ln(tant+sect)cost
So,the general solution is
y = C1cost + C2sint −ln(tant+sect)cost
r² + 1 = 0
r = i or −i
So, the complementary solution is y = C1cost + C2sint
W[y1,y2] =y1y2' − y1'y2 = cos²t + sin²t = 1
u1(x)=−∫(y2(x)g(x)/W)dx
= −∫(sint tant) dt
= sint − ln(tant+sect)
u2(x)=∫(y1(x)g(x)/W)dx
= ∫(cost tant)dt
= ∫sint dt
= −cos t
So, a particualr solution is
y = u1y1+u2y2
=[sint - ln(tant+sect)]cost − costsint
=−ln(tant+sect)cost
So,the general solution is
y = C1cost + C2sint −ln(tant+sect)cost
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MAT244--Misc / Test 1
« on: October 13, 2018, 10:10:36 PM »
I just want to make sure that as for second order differential equation, we are responsible for the homogeneous differential equation with both constant coefficients and nonconstant coefficients, and nonhomogeneous differential equation with constant coefficient, but not responsible for the nonhomogeneous differential equation with nonconstant coefficients? I have the concern since the last one appears briefly in 3.5 but the textbook says we will look into it in chapter 5.
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Thanksgiving Bonus / Re: Thanksgiving bonus 1
« on: October 05, 2018, 10:27:37 PM »
By the way, I think my answer to the original question is correct.
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Thanksgiving Bonus / Re: Thanksgiving bonus 1
« on: October 05, 2018, 09:18:48 PM »
Happy Thanksgiving.
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MAT244--Lectures & Home Assignments / model or not
« on: September 23, 2018, 09:10:08 PM »
Are we responsible for modelling in MAT244? Or we only need to know how to solve the differential equations? Thanks.
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MAT244--Lectures & Home Assignments / Re: question about the acid water problem
« on: September 22, 2018, 02:48:08 PM »
Where did you find the link? Actually, there are some direction fields but no questions on the webpage.
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