I. Obtain the general solution of the following: a) (D2 + 3D + 2)y = 1 + 3x + x2 b.) (D2 − 6D + 9)y = ex

Q: Find the general solution to y" + 7y' + 12y = 6e*. %3D

A: Consider the provided question, y''+7y'+12y=6e-xAuxilary equation…

Q: Q2 Find the general solution of y" + 5y' +6y = 4e +5sin .x.

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Q: Solve the particular solution (D2+3D+5)y = 5e-xsin2x using  D- operator method.

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Q: solve the Riccar' equanim 3 yoing the green partienten soluhon y'ax) + 1 y ₁x) +y²cx) = 4 ca).…

A: Riccati equation

Q: Specifically a differential equations problem. Question in pic below.

A: Here, y’’ +2y=-8x

Q: The solution of the IVP y = x2(1+y), y(0) =3 is O None of these. y= 4e 3 - 1. y3 xe + 3. .3 3. y36e…

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Q: Which of the following is the solution to y" – 5y' – 24y = 0 %3D a) y = Ae-3x + Be-8x b) y = Ae3x +…

A: To find the correct solution, we will all options one by one (a) y=Ae-3x+Be-8x    →(1)…

Q: A. Obtained the general solution. E... 10. (D² – 3D + 2)y = 3x²

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Q: What is the general solution of 3 (3z + y') dz – 2zydy = 0?

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Q: 5. Given that a cubic equation x" + ax" + bx +c = 0 has zerOS a, B and y. Show that aßy = -c.

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Q: 1. Give the general solution of (D5 + 2D4 + 7D3 – 4D² – 26D + 20)y = 0

A: First I have find the roots of the auxiliary equation and then according to the roots find the…

Q: Let (xp, y,) be the solution of the following equations In 2 (2x)™² = (3y)n3 3Inx = 2lny %3D Then xo

A: Given equations are 2xln2=3yln33lnx=2lny

Q: 3. Find the general solutions of, (xy +x² )dy + y²dx = 0 b.

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Q: Find a particular solution of (20) y′′−3y′−4y=2e−t.

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Q: Q(2): Find the general solution of x³y" – 3x²y" + 6ry' – by = xª In x. %3D

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Q: 1. Give the general solution of (D5 + 2D4 + 7D3 – 4D2 – 26D+20)y = 0 ="

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Q: Show that y %3D Cіx-1 + С2х + Cзlnx + 4x2 is a solution to x3y" + 2х?у" — ху' + у %3D 12х?.

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Q: Find a particular solution to 11.5e5t y" – 10y + 25y t2 +1 Yp %3D

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Q: Show that the equation 3x+4y+5z=a, 4x+5y+6z=b and 5x+6y+7z=0 do not have a solution unless a+c=2b

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Q: (1- х?)у' — ху%3D 3x(1 — х?)

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Q: Suppose that the DE y"" (x) + 7y(x) =70 2³ +123 has a solution of the form y = Az³ + B Find the…

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Q: The solution of the IVP, y' = -2xy, y(0) = 2, is: %3D

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Q: C. Use parts (a) and (b) to find particular solutions of y"- 6y' + 5y = 5x2 +3x- 16- 9e2x %3D and…

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Q: 5(a) Find the General solution of the Diffe -3x (D² + 6D + 5)y = e 3" (1 – 2sin²x) ||

A: Explanation of the solution is given below....

Q: 8. What is the particular solution of 2xyy' =1+y², when x = 2, y = 3 ? а. у%3D5x -1 C. y =V5x + 2 b.…

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Q: (a) Verify that yp, = 3e2* and y,, =x² + 3x are, respectively, particular solutions of y" – 6y' + 5y…

A: To verify the given statement and to find particular solutions by using the given statement.

Q: (D² – 3D + 2)y = e2×(1 + e2x)¯ -

A: Given: D2-3D+2y=e2x(1+e2x)-1 Formula used:y=yh+yp

Q: Find a particular solution to y" + 7y' + 10y = -19te“. %3D

A: Introduction: When there is a non-zero function of the independent variable on the right-hand side…

Q: 1. (1-х)у' %3D у?

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Q: 7. Find the general solution of (Dʻ + 2D’ + 10D²)y = 0.

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Q: The general solution of 4y"+4y' +y = 0 is ()%3D

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Q: Show that u(x, y) = y²e* + 3x² is the solution for u = yuyy + 6x . 2

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Q: Obtain the general solution unless otherwise instructed . (D² − 3D + 2)y = e²x(1 + e²x) −¹ Yc = Ур =…

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Q: Consider the following IVP: y" + 3y' + 2y = 12x²; y(0) = a, y'(0) = b Find the solution. A y(x) =…

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Q: Solve the given LDE using the method of UNDETERMINED COEFFCIENTS.  1. y''' - y' = 4e^(-x) +…

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Q: A Find the general Solution of y"ty=2xcorx -Cosx %3D

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Q: (x² – 1)y" + 2y' – (x – 1)(x + 1)² = 0

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Q: y" + 10y' + 26y =0

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Q: : Ebobl Qf solve the initiat Valu problem %3esince-2) y(an2) =a

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Q: 9. (D2 - 2D +5)²y = 0 %3D

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Q: Find a particular solution to y" + 4y + 3y = 3te". %3D

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Q: Show that y = c1ex + c2e-x + c e + 3 is a solution of y ||| -2y | | - and | + 2y = 6 (justify).

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Q: Verify that yp = 3e2x is a particular solutions of y" − 6y′ + 5? = −9e2x .

A: Explanation is given below...

Q: = 3e2x and y,, = x² + 3x are respectively solutions of у" - бу' + 5у -9е2х y" – 6y' + 5y = 5x² + 3x…

A: General solution y(g)= y(h)+y(p)

Q: 'ind the general solution of d³y 6. dr3 dy - 8y = 21e2 dr dr2

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Q: The solution of the IVP y" + 9y=0, y(0) = 1, y'(o) = 0, is %3D

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Q: c) Using the results in a) and b), give a particular solution for y" – 2y' + y = 3e* + 1+x2

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