2016 J Q2 () Express 4x + &r-5 in the form p(x+q) +r, where p, q and r are constants to be

Q: Obtain the general solution. (D² + 1)y= secx O y= C,cosx+ C2sinx + xsinx - cosxln|cosx| O y= C,cosx…

A:

Q: Which of the following is a particular solution of the equation y"+y'+7y=4cos2x? O a.…

A:

Q: Prove that there are no integer solutions (x, y, z, w) to the equation x³ +y³ 3z²+9w² +3. =

A: The given equation is x3+y3=3z2+9w2+3. We have to prove that there is no integer solution to the…

Q: Eliminate the arbitrary constants of    y= Ae^(5x) + Bxe^(5x) + e^(3x) (Ccos10x + Dsin10x)…

A: Given that y=Ae5x+Bxe5x+e3xC cos10x+D sin10x The objective is to eliminate the arbitrary constants.…

Q: 25n Evaluating sec will yield to 6 V3 A 2 2/3 B 3/3 © - 2 V3 D 2.

A:

Q: Show that y = ex + 3xex  is a solution of y"-2y'+y=0

A: The given differential equation is,

Q: 2 (ii) using Convolution theorem. (s+2)(s²+9)

A:

Q: (c) Show that V(3) = o²(X'V-¹X)-¹.

A: 3. c From the given information, y=Xβ+ε Eε=0, Vε=σ2V From the part b, β^=X'V-1X-1X'V-1y

Q: wouldn't there be a t in the second term of the general solution?

A:

Q: Max z = x1 + x2 s.t. 2x1 + x2 ≤ 20 x1 +3x2 ≤ 15 x2 ≤ 4 x1, x2 ≥ 0

A:

Q: Q.6 Show that: X-1 X+ y – 1(x-1y)= B(x,y)

A: In the given problem we have to show that                                 x-1x+y-1β(x-1,y)=β(x,y)

Q: 2. Determine the complete solution of xydy – (x + 2y)²dy = 0 %3D

A:

Q: Verify that ry4 +r - 27 = 0 defines an implicit solution of the DE dy 4ry + 2y* + 3r = 0, dr on the…

A: The function f(x) is a rule that associates or fixes a number to the particular point x. The…

Q: state where in the ty-plane the hypotheses of Theorem are satisfied 7. y′=(t2+y2)3/2

A: Given y'=t2+y232

Q: x2n+1 El-1)"; 2n +1 n=0

A:

Q: y show that = 0. . If z: x² + y² II

A:

Q: 2. x"(t) – 4x'(t) + 4x(t) = 4e²t; x(0) = –1, x'(0) = -4 %3D

A:

Q: Q2: Consider the IVP: y=1+2,1sıs2, y(1)=2.

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Let y"+ 6y'– 16y = 0, show that: %3D y = 2e-8x is a particular/exact solution. %3D

A: You have asked multiple unrelated questions in the same post. I have addressed the first one. Please…

Q: Q(2): Find the general solution of x³y" – 3x²y" + 6ry' – by = xª In x. %3D

A:

Q: 6/11 - 8) AT= 12 RT = 4x S. T %3D doesn't R

A: Given: A parallelogram STQR. As per the property of parallelogram, the diagonals bisect each other.…

Q: 8. Let a2 + xy³ + 2x = 11. Find y"(x) at the point (1, 2). %3D

A:

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

A: We have to verify that 3e-2x+4ex is a solution of y'''-3y'+2y=0

Q: Eliminate the Arbitrary Constant(s): 1. y = c,x2 + C2xe* 2. Iny = c, + C2x

A:

Q: Q5/ find y', y=In(Inx) * O y'= 1/( x-2x)*(2x)=1 O y = 1/( x-2x)*(2x)=2 none of the above

A:

Q: ind the particular solution of (9x-2yldx- x(6x- yldy-0 when x-1. y=1 To start let y-vx

A:

Q: 2. If a runner traveled a distance of d(h) = v16h4 in time t(h) = 3h – 3h - 5h2, what is the…

A: We will find the distance as following.

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: the differential equati x²y' – 2y = Inx² is cje2* + c2e¯* – x + 5 O c1x² + c2x=1 – In x + ; O 2 +…

A:

Q: 6y" – 7y' – 5y = 2x³ + e¯* – 5 -

A: Ordinary differential equation involves the derivative of single dependent and single independent…

Q: Use the IVT to prove thatx^2+ lnx =1/2 has a solution.

A: Use the IVT to prove thatx^2+ lnx =1/2 has a solution.

Q: What is r' (x) when r(x) = In (x³ + 2x2 + 3x + 1)? Select the correct answer below: O In (3z² + 4æ +…

A: Given, rx=lnx3+2x2+3x+1

Q: Exercise 0.2.12: Is there a solution to y' = y, such that y(0) = y(1)?

A:

Q: The equation X2 - 19Y² = 13 has an integral solution, i.e., there is a pair hat x2 19y2= 13. (proof…

A: We have to solve given problems:

Q: 11. Eliminate the arbitrary constants of cx? + x + y² = 0.

A:

Q: 1. Show that y = c,x1 + c,x³ is a family of solutions of x?y" - xy' - 3y = 0.

A:

Q: j. Min Z = 12x, + 8x, subject to: 4x, + 2x, 2 24 2x, + 2x, 2 10 2x, < 8 X,, X2 20

A: To solve the Linear programming problem using the graphical method  Consider the constraints as…

Q: (*") = (") + G) + 5. Prove + 2n2. %3D

A:

Q: a) Evaluate ²₁ √√1-x² √√1-x²-y²e-3(x²+y²+z²)² dz dydx

A: The given problem is to evaluate the given triple integral of Cartesian coordinates.

Q: 2 c2x-4 ( dydx 2у - 1) Q2. Evaluate the double integral x + 1

A: In this question we have to find the double integration.

Q: Show that when T(z) = Solve T(z) = ∞o if c = 0 az+b cz+d where (ad - bc #0)

A:

Q: #9a using Descartes's rule of sign

A: Given equation is,

Q: Evaluate /, a Te dydx y2 2 JJ4X-x² 32 dydx (x²+y²)' V4x-x? O 4 In(v2 – 1) – 4+7y/2 3 4 In(v2 + 1) –…

A:

Q: Verify that y = c₁ex + c₂e4x is a solution to the DE: y" - 5y + 4y = 0.

A: We are authorized to answer one question at a time, so we are answering the first one, please repost…

Q: c. St VE² + 2 dt In: Inx d.

A:

Q: 3- Prove that y=x is a solution of (x³ + 2x?)y"+ 2xy'- 2y = 0 and hence find the general

A:

Q: Let fe Cx)= Vx if osxs 4 c.(x-4)+2 if x >4 – where c denates a real constant.

A:

Q: Eliminate the arbitrary constant a from the equation (z - a) + y = a O = + 2ry' O = + 2ry Ov =+ 2ryy

A:

Q: Find дхду of z %3 In (x? - у) -2х дхду (x²–y)² 2ху дхду (x² –y)² 2х дхду (x²–y)² O. 1 %3D дхду…

A: Givenz=ln(x2-y)To find∂2z∂x∂y