7. Show that the method used in Example 5.3.2 will not yield a particular solution of y" + y' = 1 + 2x + x²; that is, (A) does'nt have a particular solution of the form y₁ = A + Bx +Cx2, where A, B, and C are constants.

Q: show that 2sin(x)3cos(x) = x has 3 solutions

A: 2sin⁡(x)3cos⁡(x)=x

Q: 3 1 x + 2. Solve: x² - x – 2 x -2" x +1, and state any NPV's.

A:

Q: Find the general solution of dy -2x6 dx y-4

A:

Q: 5) Use the method of undetermined coefficients to find a solution to y"+y-6y=5Kte-t for a constant…

A:

Q: d. The linear Diophantine equation ax + by = c has a solution if and only if dc. Let xo, yo be any…

A:

Q: . Find the general solution of the first-order equation y? – 2ry dy dr

A:

Q: Find a real solution of the equations x²-5x+4=0 3xy²-10y+7=0 nitial approximation as (0.5, 0.5).

A:

Q: A 2nd order homogenous LDE has a solution xe-3x Find its general solution.

A:

Q: 4. Suppose the following functions are a general solution of: y(4) + a3y/" + azy" + a;y' + a0y = 0

A:

Q: 7. Use Romberg method to calculate 2dx.

A: Romberg Integration is given as :-I=∫abf(x)dx=Rn k+O((b−a2n)2k+2)R0 0R1 0R1 1⋯⋯⋱Rn−1 0Rn−1 1⋯Rn−1…

Q: Show that r =1+i, x2 = 1- i is a solution of (3+ i)x1 + (1+ i)x2 = 4 + 4i

A: The solution is given as

Q: 2:2 + [3] x + 2 = [0] in Z6.

A: The solution given below with attached file.Explanation:

Q: 9. The general solution of x' = -6 -4 x is: 2 | ++(-:)| (a) x = Cịe-2t + Cze¬2t (b) x = Cye" () +…

A:

Q: Which of the following is a general solution to the following: x²y" + xy' + (36x² − 1) y = 0 A. y =…

A: Solution:

Q: 2x Example: Show y = ae¯* +be* is a solution of = de y"-y'-2y 0 for all values of a and b. %3D

A:

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

A:

Q: Verify that yp, =3e²x and yp₂ = x² + 3x are, respectively, particular solutions of y" - 6y' + 5y =…

A:

Q: independent solutions of y''+ P(x)y'+ Q(x)y = 0. Assume that f1(x) has at

A:

Q: Suppose that x-y" + axy' + by = 0 has the general solution of the following form: y = C,x³ + C2x³ In…

A:

Q: 2a) find a solution of y" (x) = y(x) that passes the origin and go trhout the point (In(2),-).

A:

Q: 2. Show that x4 - 3x - 1 has a solution between 1 and 0, and another solution between 1 and 2.

A:

Q: 6 - Show that x(t) = (C1 + C2t) e¬t is a valid solution to i + 2yi + 7²x = 0.

A:

Q: 3. 2хydx - (3xу + 2y?)dy %3D0 o (x - 2y)*(2x +y) = c O (x - y)*(x + y) = c (х + 2y)(2x - у)*- с о…

A:

Q: Find a particular solution to -18.5e-2t y" +4y +4y = 12 + 1

A: Introduction: A differential equation is an equation that contains the derivative of an unknown…

Q: If y1, Y2, and y3 are any solutions of y" – 6y' + y = 0, then so is 4y1 – y2 +y3 -

A:

Q: Determine three linearly independent solutions to the equation y" + 2y" – 3y = 0 of the form y(x) =…

A: The given differential equation is                                                y'''+2y''-3y'=0

Q: (3) The approximate enrollment, in millions between the years 2009 and 2018 is provided by a linear…

A:

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: Let (x, y,) be the solution of the following equations In 2 (2x) = (3y)m3 3Inx: = 2Iny Then is

A: This is very complicated & lengthy problem.So I can do it in Advanced Mathematics.

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: y" + 3y² + 2y = 12x²; y(0) = a, y'(0) = b Find the solution. A y(x) = c₁e²x + c₁₂e-2x+6x³-18x²+2 B)…

A: Given initial value problem is- y''+3y'+2y=12x2   ; y(0)=a , y'(0)=b We have to find the solution of…