Solve 4xy' — 20y = x¯¹, given y(1) = −3. First, identify the integrating factor, r(x). r(x) = ☐ help (formulas) Now find the general solution. y(x) = ☐ help (formulas) Note: Use C for the arbitrary constant. Finally, solve the initial value problem y(1) = −3. y(x) = ☐ help (formulas) Book: Section 1.4 of Notes on Diffy Qs

Q: there a way to check if the equation you find after applying the initial condition is correct?

A: Let  Given that dy/dx = 2x (y − 1),.      y(0) = y0. And from solved answer The general solution is…

Q: (8x'y*) (-4x"'y) * (2x°y¯³)-

A: 8x3y-4-2-4x-1y-32x5y-3-2=-4x-1y32x5y-328x3y-42 [we first get rid of the negative signs from the…

Q: Find the general solution of the differential equation: y+2y = test Use lower case c for the…

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Q: Find the general solution by undetermined coefficients.  y'' + y = 2x2e-x.

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Q: Q1// Use Tow Phase method to solve the Mathematical model (Stop at Table 1 in Stage Two) MinZ…

A: The given LPP is, Min Z= x1-2x2s.t.       x1+x2≥2          -x1+x2≥1                   x2≤3and…

Q: The general solution of y' x2 can be written in the form

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Q: 40e5*, y(0) = ;, y'(0) =y"(0) 9. y" – 2y" + y' = 2 – 24e* + 2

A: Given: y'''-2y''+y' = 2-24ex+40e5x, y(0) = 12, y'(0)=52, y''(0)=-92

Q: solve y''-y'=xex  using undetermined coefficient. The characteristic equation will be r2-r=0

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Q: where y1 = e* is one of the functions in the fundamental solution set. - %3D xy" + (2-2x)y' +(x- 2)y…

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Q: Find the d. c. of T from definition.

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Q: 3. a) Define Integrating Factor and Exact Differential Equation. b) Solve: (x2 + xy-y² )dx+ x² - 2xy…

A: "Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Example 4: Solve i) у" - 2у' + у 3 Зсохх + 2sinx.

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Q: Can you elaborate how to incorporate c into the solution. Like c=0? And how does f'(0)=7 and…

A: Solution below

Q: Q1: If y" + y = x², then yp = Q4: The solution of y(4) - 5y" + 4y = 0 is: (B) c₁e* + c₂ex +…

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Q: x?S(x x] =0 2 2 x Can be wpitden as s" (o)= the Solu tion is

A: Note:- You have mistakenly written it as c1e^ax + c2e^-ax. At the place of a there will be α.

Q: S(x) = 2x" + 4x + 2x + 1 g(x) = (x + 1) Find (fg)(- 1)

A: Given  f(x) = 2x3+4x2+2x+1 g(x) = (x+1)   We have to find (fg)(-1).

Q: FIND THE UNEAR DIFFERENTIAL OPERATOR THAT "ANNIHILATES THE FUNCTION, (x + 3xe6x)

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Q: Solve 1og x t1og (x-2)= 10q (ex)

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Q: Find a linear model, g(t)=mx+b, and an exponential model, g(t)=ab^t, if g(0)=5 and g(-2)=10. (Round…

A: Here the exponential model is given. So from that, we will find the value of a and b. then solving…

Q: Solve 1 0-²40 = 5 x (0) = - 4, y(0) = 10

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Q: -1 -1 3. Find a particular solution of x' = -2 2 x+ 4 -1 -2 et

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Q: 7 0-3 -9 -2 3 18 0-8 y, y(0) = 2 3

A: Given y'=70-3-9-23180-8y Also given y0=23-1   To reduce to row echelon form and solve for constant…

Q: 5. Given: f (x) = ax³ – 9x² + 2x – 4 and g(x) = bx³ – 5x² + 62x + 70 | Solve for all values of a and…

A: We have to find

Q: Consider the estimated quadratic model   y ^ = 23 + 1.6x − 0.02x2. Now, Predict y when x equals 10,…

A: The objective is to find Predict y when x equals 10, 20, and 30.

Q: Find the values of a, b, c, and d when f(x) = ax3 + bx2 + cx + d and the following conditions are…

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Q: Solve 24-4x²³/dx + xdy = 0 using the integrating factor M = 2² SPOXK

A: Solve 2(y - 4x2)dx +x dy=0, Using the integrating factor μ=e∫P(x) dx.

Q: A virus is believed to be spreading through a sheep farm according to that equation N = 450 (11 +…

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Q: If u(x) = x3, then du = 3x2.

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Q: y" + 2y'-3y 7x-3x.

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Q: x+1 Solve y'=- y +1

A: Differential equation