7. Show that the equation p(x) = q(x)m(x) + R(x) is equiva- lent to the equation p(x) = m(x) + R(x) for all x for which 9(x) 9(x) q(x) is nonzero.

Q: 1) Use reduction of order method with y₁ (x) = e³x to find a second solution y2 for the DE: y" - 9y…

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Q: Consider the following IVP: x" - 4x' + 4x = 4e2t; x(0) = -1, x'(0) = -4 Find the general solution. A…

A: Given Differential equation is x'' - 4x' + 4x = 4e2t

Q: 1/4 using the Linear Approximation L(x) of f(x) x14 at a = 16 Approximate 181/4 (Use symbolic…

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Q: 5. Eliminate the arbitrary constant on the given equation: -4xy2 + xy. C

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Q: Problem B1: Prove that for all x E R sufficiently large, r³ – 7x > 4x2 + 2. -

A: That's easy. Thumb up. Have a good day!!!

Q: ,2k 101. Let F(x) = 2k . k! k=0 (b) Show that y = F(x) is a solution of y" = xy' + y. y(0) = 1,…

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Q: a. My =n xyy

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Q: What is the particular solution for y′=−2e^x−3x^2+x−4 such that y(0)=1?

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Q: The solution of y2 – x²y' = 0 with IVP (1)= . is given by y(x) = 1+x 1 y(x) = 1+x 1 y(x) = 1+ x2 (x)…

A: Given initial value problem y2-x2y'=0    ; y(1)=12

Q: Q4: Use the Gauss-Seidel iterative technique to find approximate solutions to 10x -x +2x3 -x +11x2-…

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Q: (a) First find the general solution of y" – 5y + 6y = 2e* (3) by using the Undetermined Coefficient…

A: Introduction: A higher-order linear non-homogeneous differential equation has two solutions. One is…

Q: Find a general solution of y"- 2iy'+3y= 0.

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Q: - 3)²y" (x) - 3(x-3)y'(x) + 3y(x) = 2(x-3)^e², x > 3. Verify that y₁(x) = (x-3)³ is a particular…

A: Given the differential equation: x-32y''x-3x-3y'x+3yx=2x-34ex To find the solution of above…

Q: Suppose that Yı x5 is a solution to x²y" – 10xy' + 30y 0. Use reduction of order to find another…

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Q: Q1 Find the general solution of the PDE uuz + (x + u)u, = x

A: The given pde is : u ux +(x+u) uy =xComparing it with P.dudx+Q.dudy=RSo we get ,P=uQ=(x+u)R=xNow…

Q: 6. Find the general solution of (x+ 2y- 1) dx + (x + 2y + 5) dy = 0 x - y + 6 In(7 - x - 2y) x + y -…

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Q: Is y(x) = C1sin2x + C2cos2x, where C1 and C2 are arbitrary constants, a solution of y” + 4y = 0?

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Q: 23. If u = f(x), then +2x² + 1 k + C for some constant k . x² + 1 Compute kf (1). (a) ¼ (b) – ½ (c)…

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Q: A) (:: :) Verify that y = c₁cos(3x) + c₂sin(3x) is a solution of y' +9y = 0

A: Note: As per our company guidelines we are supposed to answer the first question only. Kindly ask…

Q: 4- Find the particular solution for: 3x²y' = 5x – 6xy, x = 2 when y = 1 %3D

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Q: Verify that yp = x2 + 3x is a particular solutions of y" − 6y′ + 5y = 5x2 + 3x − 16

A: To verify yp=x2+3x is particular solution of  y''-6y'+5y=5x2+3x-16       (1)

Q: B. Solve the following LP algebraically. а. Max Z= 150X+ 160Y subject to: X+ Y 20 Y> 15 Χ. Y>0 b.…

A: We solve the first two problem by simplex method. In this problem we first transform the problem…

Q: 4. Find the critical values of Z = 12x2 – 18x - 8xy - 26y + 9y2 + 40 and check whether the equation…

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Q: 4. Find for the particular solution of y' = x3 – 2xy when x = 1, y = 2 %3D

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Q: 28.If the Wronskian of any two solutions of y″ + p(t) y′ + q(t) y = 0 is constant, what does this…

A: Concept: The calculus helps in understanding the changes between values that are related by a…

Q: der the problem maxx + 2y subject to x² + y² ≤ 1 and x + y 20

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Q: Use the theorem of Leibniz in the following problems: If y=x³e2x find y(m) and hence y(3). julm) =…

A: Leibniz rule states that (f(x)⋅g(x))n=∑r=0n Cr nf(n−r)(x)⋅gr(x) Let fx=e2x and gx=x3

Q: Find the general solution of: az əz 2, дх ду (1+ /z- x – y)

A: The given equation can be written as: 1+z−x−y∂z∂x+∂z∂y=2dx1+z−x−y=dy1=dz2          ......i

Q: 24.Find all values of α for which all solutions of x2y′′+αxy′+52y=0x2y″+αxy′+52y=0 approach zero as…

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Q: Find a generating function for the number of integer solutions of 2x +3y+ 7z =r with (a) x, y, z > 0…

A: Here, we need to find a generating function for the number of integer solutions of 2x+3y+7z=r  with…

Q: 4 Find the general Solution of the following PDES • з Их + 2 Иу -Х u(x,c) =4е 2 (зу-2х)12 ans3- и(x,…

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Q: Now 25 -> 25 X9 >9 (n- 6X+) +25 (y=4y+1) = 225 -> 9n2-54X+ 81+ =>9n+25y54x-1004+181-225= 25y? 100y+…

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Q: Find the general solution of ди ди (y – z) + (x – z) ди + (2y – 2x) ду - az

A: The differential equation is given as (y-z)∂u∂x + (x-z)∂u∂y  + (2y-2x)∂u∂z = 0 We will solve it by…

Q: 3. Verify that 3e 2x + 4e* is a solution of the y"-3y'+2y=0.

A: We have to verify if the given is a solution to given differential equation or not.

Q: Solve the following LP problem using graphical method. Max z = 3x₁ + 4x₂ Subject to 2x₁ + x₂ < 10 x₁…

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Q: 8) (a). (8pts) Find a general solution to y" – 6y' + 9y = t-³e³3t by using variation of parameter…

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

A: eular method

Q: Find the general solution to the homogenous DE y'-16у' + 64у %3 0

A: The given homogeneous DE is y''-16y'+64y=0. The auxiliary equation is m2-16m+64=0.

Q: Prove that the general solution to L(y)=(x) is y=Yh+Yp

A: Definitions:  yh is a homogeneous solution so, for any yh, Lyh=0.  yp is a particular solution so,…

Q: = (y² – z² +3yz – 2x of the following is/a

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Q: 6. Find the general solution of (x + 2y – 1) dx + (x + 2y + 5) dy = 0 x - y + 6 In(7 - x - 2y) x + y…

A: Answer is option D)

Q: Verify that y = c1x+c2Vx+ is the general solution of the 6x following nonhomogeneous 2.²y" – xy' + y…

A: Derivative of xn: Derivative of an exponential function that is, xn is given by the formula,…

Q: A particular solution of x¨ − 3x˙ + 2x = t2 + 1 is given by

A: given that x''-3x'+2x=t2+1. we need to find the particular solution for the given differential…

Q: (b) Show that for x > 0 and k + 0 the equations In x x* = e* and 1 have the same solutions

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Q: Show whether the two equations y₁ = using the Wronskian. 12e and y2 1.2e are independent or…

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Q: Find a general solution to (x+1)x²y" + xy - (r+1)³y=0.

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Q: 10. Find the particular solution that satisfies the initial condition. xy'+ 2y = 3x² – 5x. Initial…

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Q: 22. Find the particular solution for he non-homogen 1st OLDE using undetermined coefficient method,…

A: Differential equation system.

Q: 1 Find the general solution of x'y" +xy' -y= x+1

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Q: 4) Prove that y = x-3/2 is a solution to 4x2y" + 12xy' + 3y = 0.

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