3 Math Questions (ODE) - Answer any of them please.?

Question

Ok i got an assignment and I can't get these 3 questions. If anyone could answer and of them that'd b great.

1. du/dt = e^(-4t + 3u), u(0) = 8
Solve for u = ?

2.dy/dx – 6tan(3x)y + 5cos(4x) = 0 y(0) = 1
The solution y(x) = ?

3. x*dy/dx – 7y= x^20 y(1) = 7
y = ?

Thanks in advance.

Answer 1

[PDF] Final Exam Review Math 1100-005File Format: PDF/Adobe Acrobat - View as HTML
3u. 2. du. =. u. 4. 4 −. 3u. 3. 3. u=8. u=4. = 512. (d). ln(x ... u = 500 + t. v =. e. −. 03t. − .03. du = dt. dv = e ...
www.math.utah.edu/~smith/math1100_documents/final_rev_solns.pdf - Similar pages

[PDF] MAT 126 Calculus B Spring 2006 Practice Midterm II SolutionsFile Format: PDF/Adobe Acrobat - View as HTML
du = 3u. 1. 3. 27. 1. = 3(27). 1. 3. − 3 = 3 · 3 − 3 = 6. (b). π. 2. 0. e. sin x. cosxdx. Solution. Substitution u = sinx gives du = cosxdx and ...
www.math.sunysb.edu/~leontak/126-S06/Practice126-2-S06-Sol.pdf - Similar pages

[PDF] MAT 126 Calculus B Spring 2005 Practice Midterm II SolutionsFile Format: PDF/Adobe Acrobat - View as HTML
0. 2. (2x + 1). 2. 3. dx =. 27. 1. 1. u. 2. 3. du = 3u ... We use integration by parts with u = t and. dv = e. t. dt. We have du = dt and v = e ...
www.math.sunysb.edu/~leontak/126-S05/Practice126-2-05-Sol.pdf - Similar pages
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[PDF] On the regularization of functional equationsFile Format: PDF/Adobe Acrobat
3u z. du/dt]Qo. = 2(1 - 3312 - 3132) 6(t) = 0. g--'O. Thus u = /(t) is a solution of(l) ... [t d2u/dt = +. 3u 2. du/dt],,. 3et 2 ]t 2. (8). -. 2(t2+e)5/2 + ...
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Answer 2

1.
du/dt = e^(-4t + 3u) = e^(-4t)*e^(3u)
This is a separable differential equation.

moving the u's to one side and the t's to the other, we get:
e^(-3u)du = e^(-4t)dt

integrating both sides gives us:

(-1/3)*e^(-3u) = (-1/4)*e^(-4t) + C

Now the big job is to solve this for u:
e^(-3u) = (3/4)*e^(-4t) + C
taking the ln of both sides gives us:
-3*u = ln((3/4)*e^(-4t) + C)
and finally:
u = (-1/3)ln((3/4)*e^(-4t) + C)

You can now plug in t=0 and use your initial condition to find C.

3.
First step: get this problem into standard form by dividing every term by x.
dy/dx – 7(1/x)y= x^19

With an ODE of this form, we should first try to calculate an integrating factor.
IF = e^(integral(-7*(1/x))
=e^(-7*integral(1/x)) = e^(-7*ln(x))
using properties of logs, this is equal to:
e^ln(x^(-7)). The power and the log cancel out, and our IF is x^-7.

We now multiply each term in the equation by this factor:
(x^-7)*dy/dx - 7x^(-8)*y = x^12

The left-hand side is now the derivative of a product:
((x^-7)*y)' = x^12

Now we can integrate both sides:
(x^-7)*y = (1/13)*x^13 + C

The last steps are solving for y, then plugging in x=1 and using your initial condition to find C

Answer 3

wow, good luck. i have no idea