B. NONHOMOGENEOUS EQUATIONS: UNDETERMINED COEFFICIENTS 2. (D2 + D – 2)y = 2x – 40cos2x 3. (D² + 1)y = sinx

Q: Solve: (3x – 2xy+ 3y)dx = 4rydy (y +3x)(y – x)3 = Ca³ %3D O (y + 3x) (y – x) = Ca³ (y – 3x)(y + x)3…

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Q: e equation y-x+6x=18 fill in the steps to write the equation in standard form. %3D PENCIL THIN BLACK…

A: Here we have to write the given in the standard form.

Q: 2y′ + y = 3t2

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Q: Solve, (2x+3y-2)dx+(3x-4y+1)dy = 0 %3D

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Q: Solve 2- (2xy - 2y)dx + (3x'y-4x)dy 0

A: We have to solve given problem:

Q: Solve (D5 – 2D4 + 4D³ – 8D²) y = 48e-2 16 sin (2x) - = A- B I = E E E P & O

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Q: B) Solve (3x? + 3x y²)dx + (3x²y – 3y² + 2y)dy = 0 %3D

A: First test for exactness:  ∂∂y3x2+3xy2=6xy ∂∂x3x2y-3y2+2y=6xy Since, ∂∂x3x2y-3y2+2y=∂∂y3x2+3xy2 so…

Q: Eliminate the arbitrary constant. y=Ax 5 + Bx3

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Q: a va?-x? a²-x² (x + y) dydx

A: We have to find the value of given intregation.

Q: Solve for Z. X= (Y-Z) 3

A: Given: X=23Y-Z We have to solve for Z.

Q: Eliminate the arbitrary constant. y=Ax 5+ Bx³ A B 7xy "- x²y + 15y = 0 D x²y '- 7xy "+15y = 0…

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Q: S,(2x-y)dxdydz

A: Consider the integral: ∫12∫0z2∫0y-z2x-ydxdydz

Q: 2- Solve (4x + 2y + 3)dx - (6x + 3y – 2)dy = 0.

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Q: 2(2x² + y²) dx - xy dy = 0

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Q: Solve the following first order equations: (a) (x²y² + 1)dr + 2r²dy = 0, use the substitution ry =…

A: We have to solve 1st order differential equation using substitution xy = u.

Q: eliminate the parameter to obtain an equation in x and y

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Q: Solve y′′+ 9y = 3sin(3t)

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Q: Find the solution. (Dé+ 9D* +24D² + 16)y = 0. y = c,cosr +c,sinr + (c,+cx)cosr+ (cz+cx) sinx y =…

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Q: Suppose you are climbing a hill whose shape is given by the equation z = 900 - 0.005x north. 0.01y,…

A: Directional derivative of a function f(x,y,) in the direction of unit vector  u^=ai^+bj^  where…

Q: Solve for y. x= (3y+5)/(7y-1)

A: To solve for .

Q: solve (x? + y) dx + (y³ + x) dy = 0. A yª + x + B + x + y + (c) = C ,3 3/7 3/4

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Q: Solve (2xy-2xy- = 0 4xy² +2x) dx + (3x2y + 4y) dy %3D

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Q: Find all solutions to the equation (D² – 3D + 2)y(x) = 2e³".

A: Given differential equation is (D2 - 3D + 2)y(x) = 2e3x

Q: Find y′′ y = -3x4(4x+6)2

A: Recall: Power rule; dxndx=nxn-1 Given, y = -3x4(4x+6)2

Q: 2 (√x² + y²) [2x − (x² + y²)]

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Q: (2x-4y)dydx 3.

A: