8. Find the particular solution of x²y"+ xy' = 1; y = 0 and y' = 1/2, when x = 1.

Q: B. Solve x' = 01 1 54 x + 12e4t 18e4t

A:

Q: y" − 4y = 10

A: The given differential equation is y" − 4y = 10. Its auxiliary equation is m2-4=0. Obtain the roots…

Q: (2xy² + 2y) + (2x²y + 2x)y' = 0

A:

Q: Differentiate. y = In (6x? - 5x + 3) y' =O

A: Given: y=ln6x2-5x+3 We know that ddxlnx=1x…

Q: Determine all solutions. y'= (x-y + 3)²

A:

Q: + ¹² = 4t, where y'(1) = 1 and y(1)=2. 4) Solve y" +

A:

Q: 2yy" = 1 + (y')² 2

A:

Q: х? + 2х + 9y? — 18у + 11 3D 0 Is the equation of: Select one: О а. Нурerbola O b. Ellipse O c.…

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

Q: Find the general solution y''-y'-2y=0

A: Given the differential equation y''-y'-2y=0. We need to find the general solution of the above…

Q: Solve y'' − 4y' + 4y = 3e2t

A: Solve y'' − 4y' + 4y = 3e2t

Q: Find a particular solution y'''-y''-4y'+8y=6xe^2x

A: y'''-y''-4y'+8y=6xe^2x Particular integral = 6xe2x 6xe2xD3-D2-4D+8By using property shift F(D) to…

Q: Find y'. y=(4x-4)(2x+1) OA. 16x-2 B. 8x-4 OC. 16x-12 OD. 16x-4

A:

Q: Differentiate. y = ³√√x³+3x+1.x4

A: Given function y = x3 + 3x + 13.x4

Q: 4x2y''−8xy'+9y=0, y1=x3/2

A: See the attachment

Q: Solve x'y-5xy+13y-0

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Q: 5. Find y'. y = 3x² – 14x + 42

A:

Q: Find y'. 9) y = (5x-2)(3x + 1)

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Q: Find y' implicitly. 1. (x + y)² = 4y 2. (x + 2y)² = x + 10 of 1

A:

Q: Solve  y'' − 2y' + 5y = x2 + 1

A: Solution

Q: Solve for y' 4xy+ y² 2x2 –2y

A: The objective is to solve y'=4xy+y22x2-2y. The equation can be written as, -4x+yy+2x2-2yy2y'=0 The…

Q: Solve x³y"+6x²y"+4xy' = 0.

A:

Q: Find General Solution of y" + y" = 0.

A: Given the differential equation is y"' + y" = 0. Here the auxiliary equation is m3 + m2  = 0