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mihalych1998 [28]
3 years ago
11

Use the method of reduction of order to find a second solution to t^2y' + 3ty' – 3y = 0, t> 0 Given yı(t) = t y2(t) = Preview

Give your answer in simplest form (ie no coefficients)
Mathematics
1 answer:
Anestetic [448]3 years ago
6 0

Let y_2(t)=tv(t). Then

{y_2}'=tv'+v

{y_2}''=tv''+2v'

and substituting these into the ODE gives

t^2(tv''+2v')+3t(tv'+v)-3tv=0

t^3v''+5t^2v'=0

tv''+5v'=0

Let u(t)=v'(t), so that u'(t)=v''(t). Then the ODE is linear in u, with

tu'+5u=0

Multiply both sides by t^4, so that the left side can be condensed as the derivative of a product:

t^5u'+5t^4u=(t^5u)'=0

Integrating both sides and solving for u(t) gives

t^5u=C\implies u=Ct^{-5}

Integrate again to solve for v(t):

v=C_1t^{-6}+C_2

and finally, solve for y_2(t) by multiplying both sides by t:

tv=y_2=C_1t^{-5}+C_2t

y_1(t)=t already accounts for the t term in this solution, so the other independent solution is y_2(t)=t^{-5}.

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8 0
3 years ago
Katie is building a rectangular wall. The wall will be 332 bricks wide and 39 bricks tall. She has 15,000 bricks. Does she have
agasfer [191]
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4 0
3 years ago
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Can someone please explain how the answer to this is, "19 and 3", "1 and 12"
Makovka662 [10]

Using the image given, the angles that are Alternate Exterior Angles are: 1, 2, 3, 4,13,14, 18, 19.

<h3>What are Alternate Exterior Angles?</h3>

These are known to be the Alternate exterior angles that are regarded as the pair of angles found on the outer side of the two parallel lines but they are seen on the opposite side of the transversal.

Note that in the image given, there are two parallel lines and two transversal lines.

Note also that to get the Alternate exterior angles, it has to be the angles seen on the seen on the opposite side of the transversal that has crossed the parallels lines and from the image given, only angle 1, 2, 3, 4,13,14, 18, 19 fit into the description.

Therefore, Using the image given, the angles that are Alternate Exterior Angles are: 1, 2, 3, 4,13,14, 18 19.

Learn more about Alternate Exterior Angles from

brainly.com/question/2398628

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5 0
2 years ago
Help me please with this question
Gelneren [198K]

You could go both ways with this question, and they're both true:

-- circle "greatest" in both places;

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3 years ago
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masha68 [24]

Answer:

I belive it is (40x10)+(40x7)+(3x10)+(3x7)

Step-by-step explanation:

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