• Verify that 3r is a one-parameter family of solutions of the DE ry + y = 3r. • Deduce a solution of the IVP ay +y = 2r, y(1) = 2, and find its interval of definition.

Q: Find a second linearly independent solution and write down the general solution: x²y" - 5xy' +9y =…

A: To find a second linear independent solution of the given problem where one solution is given.…

Q: The values of C, and C₂ so that y(x) = C₁x + C₂ (-) satisfies the two conditions y(1) = 1 and y'(1)…

A: Given: yx=C1x+C2-13x2 To find the values of C1 and C2 such that y1=1 and y'1=-1.

Q: If yo is the solution of the equations xy' + 3y = 2x, y(1) = 8, determine the value of yo(2).

A:

Q: Consider the following (x²-3x+1)y" -(x²-x-2)y'+(2x-3)y=0 on the interval I = (3,00) Verify that Y₁…

A:

Q: Prove that 14n is not O(12n)

A: Note that a function f(n) is big O(g(n)) if f(n) is less than constant times g(n) for large n. This…

Q: 5. Solve the equation * SHOW YOUR COMPLETE AND CLEAR SOLUTION. (»^)² + (x – 2x+ ) y' +x--xt = 0 |…

A:

Q: 3(3y² + x²)dy - 2xydx = 0 when x = 3, y = -2

A:

Q: Find two linearly independent solutions of 2x²y" - xy' + (−3x + 1)y = 0, x > 0 = x¹¹ (1 + α₁x + a₂x²…

A:

Q: 6z dy (78)a

A:

Q: This problem is about the constant coefficient linear inhomogeneous equation p(d/dx)y = f(x) where…

A: “Since you have posted a question with multiple sub parts, we will provide the solution only to the…

Q: 3. Is y(x) = C,sin2x + C2cos2x, where C1 and C2are arbitrary constants, a solution of y" + 4y = 0?

A:

Q: 3. If X is a solution of the IVP X': Х, X (0) — %3D %3D then X %3D

A:

Q: Solve for the general solution of (D: - 5D + 6)y = 4e* using method of undetermined coefficients.

A:

Q: Let y1, Y2 be two independent solutions of (t 1)y"- ty' +y = 0. If W(y1, Y2)(2) = e2, then W(y1,…

A:

Q: Find general solution of (4x + 6y)dx + (8x + 12y − 6)dy = 0 (DE WITH COEFFICIENTS LINEAR IN 2…

A: We have to solve given problem:

Q: а. у' +3у%38, у(0) %3D4 b. 1 xdx+dy= 0, y(0)=8 y c. senxdx+ ydy=0 y(0)= -2 d. y' +2xy2 = 0, y(0) = 3

A: y = -srqt(2+2cosx) is a solution of:

Q: Let f(x, y) = x² – y?. Find (c) The linearization of f at the point (2, –3).

A:

Q: A particular solution of x²y'- x(x + 2)y' + (x + 2)y=2x³, x>0, y₁(x)=x, V₂(x) = xex

A: The given differential equation is, x2y''-xx+2y'+x+2y=2x3rewriting it ,we…

Q: Find all equilibrium points and determine their types when C =1. *, = x2 *, = -bx, +1+ c(-1+ sat…

A: Given: x.1=x2x.2 =-bx2+1+c-1+sat0.5-x1-x2

Q: The solution to the IVP (x² + y²) y'+xy=0 with y (0) = 2 is y (2x²-y)=4. y²(2x² + y²) = 16. Oy²(2x²…

A: The given problem is to find the solution for the given initial value problem with given initial…

Q: ht) Consider the discrete-time dynamical system Xr+1 - What is the equilibrium for this system? What…

A:

Q: ) Find of the implicit function a? + 5xy + y? – 2x + y – 6 = 0 at the point 1. . (1, 1).

A: Topic:- derivatives

Q: Find two linearly independent solutions to the Cauchy-Euler equation ²y" - 3xy' + 3y = 0. (ii) Use…

A: Cauchy Euler's differential equations

Q: Determine the largest interval in which the unique solution of (t - 3)y +tan ty = t, y(n) = 0 is…

A:

Q: (c) Consider the double integral || xy dA where D is bounded by the x-axis and the upper half…

A:

Q: =² + 2y²) = ry, y(-1) = 1 dy O 2n* = y² + a? O a* = 4 (y² + a²) O a4 = 2 (y² + x²)

A:

Q: (9) Solve the following diserental equation dy dx 2 3+y 3.x 3-y = (9x - y²x), y(0) = 0 Answer: = e

A:

Q: Find two linearly independent solutions of 2x2y"-xy'+(-6x+1)y=0, x>0 of the form

A:

Q: Solve for the general solution * (4xy+3y – x) dx + x (x + 2y) dy = 0 x' (4xy² + 4y – x) = c x²…

A:

Q: y=cJ,(/2x) +c,J,(/2x)is solution for x?y "+xy'+ (2x² – 4) y=0

A: Given, y=C1J42x+C2J42x is solution for x2y''+xy'+2x2-4=0 To find that this statement is true of…

Q: solve the following second order differantial equation. (9D² +30D+25)y = 0 33 - D: derivative…

A:

Q: Find the maximum value of f(x1,2,,xn) = (x₁ - x₂ ... n)¹/" where x₁,..., In are positive numbers and…

A: (a) Maximize?(?1,?2,...,??)=?1?2...??n subject tog(x1,x2,...,xn)=x1+x2+.........+xn=cand xi>0By…

Q: Find two linearly independent solutions of 2x²y" - xy' + (-1x + 1)y=0, x > 0 of the form y₁ = x¹(1 +…

A:

Q: Let a,b be constants, a 0. If Y = aX +b, show that p(X, Y) = lif a > 0 p(X,Y) = –1 if a < 0

A: It is given that Y = aX + b We have to calculate the correlation coefficient between the variables X…