Find the G.S. of the Riccati DE and the solution of the IVP (both must be written in the explicit form): Sx3y' + x2y = y2 + 2x4 {x?y' + y(1) = 2 Page 1 of 2 given that yı = cx2 is a particular solution for the Riccati DE.

Answers

Answer 1

The general solution (G.S.) of the Riccati DE is y(x) = cx² + u(x), and the explicit form of the IVP solution is y(x) = cx² + (2 - cx²)/x².


1. Rewrite the given DE as: y' = (y² + 2x⁴ - x²y) / Sx³.
2. Given that y1 = cx² is a particular solution, substitute it into the DE to find the constant c.
3. The general solution is y(x) = y1 + u(x), where u(x) is another function to be determined.
4. Substitute y(x) = cx² + u(x) into the DE and simplify the equation.
5. Recognize that the simplified equation is a first-order linear DE for u(x).
6. Solve the first-order linear DE to find u(x).
7. Combine y1 and u(x) to obtain the general solution y(x) = cx² + u(x).
8. Use the initial condition x²y' + y(1) = 2 to find the explicit form of the IVP solution.

To know more about explicit form click on below link:

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Related Questions

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o
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Answer:

2

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

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m=-4/(-4+2)=-4/-2=2

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Answer:

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Step-by-step explanation:

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Step-by-step explanation:

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Step-by-step explanation:

That's how I end up on harvard.

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Answers

46 degrees for both b and c

Answer:

46 degrees for both b and c

Step-by-step explanation:

the vertical angles postulate means that the opposite angle must be the same, so 134*2=268

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using the vertical angles again, b and c are the same, and the sum must be 92

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If an object is dropped from 100 feet in the air and air resistance is ignored, the object will fall at a rate that can be modeled by the function h(t) = -16t? + 100. After how many seconds is the object 20 feet from theground?

Answers

every foot is a second hope that helps

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Step-by-step explanation:

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Step-by-step explanation:

You would just set each side equal to its opposite so for x, it'll be like:

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I attached my work below as well to help you.

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Answer:

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Step-by-step explanation:

original answer: 0.74511316047

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Step-by-step explanation:

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pa help po need lang ipasa ngayon​

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1.

[tex] \frac{3}{5} \times \frac{5}{6} = \frac{15}{30} = \frac{1}{2} [/tex]

2.

[tex] \frac{3}{5} \times \frac{3}{15} = \frac{9}{75} = \frac{3}{25} [/tex]

3.

[tex] \frac{5}{8} \times \frac{4}{10} = \frac{20}{80} = \frac{1}{4} [/tex]

4.

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5.

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8.

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10.

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Answers

Step-by-step explanation:

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I need help quick I'll give brainliest!

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Answer:

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Step-by-step explanation:

Put the following equation of a line into slope-intercept form, simplifying all
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Answer:

مرحبًا ، سأكون سعيدًا لمساعدتك في حبك في العمل ، وأريد المزيد من التفاصيل ، وسأبذل قصارى جهدي لإرضائك

Step-by-step explanation:

pls solve~~~~~~~~~~~~~~~~~~~~~~~~​

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Step-by-step explanation:

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

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Here's another way you can do it:

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Step-by-step explanation:

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Answers

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Step-by-step explanation:

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Answers

Answer:

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Step-by-step explanation:

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Step-by-step explanation:

GOOD QUESTION BRO

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I did not knew what you wanted, but I think this is what you wanted.

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Answers

Answer:

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Answer:

12=6

Step-by-step explanation:

well i evaluated it, snd thats what i got

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