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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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My answer to c is slightly different.

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Can you show me the detailed integral of y2?

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Can anyone explain the integral here? I tried by parts but don't know how.

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What's the strategy to choose from using the undetermined coefficient method or variation of parameters method?

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What's the strategy to sketch a graph of the solution in the x1- x2 plane for t>0?

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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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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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By the way, I think my answer to the original question is correct.

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Happy Thanksgiving.

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Are we responsible for modelling in MAT244? Or we only need to know how to solve the differential equations? Thanks.

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Where did you find the link? Actually, there are some direction fields but no questions on the webpage.

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