45. f(x) = 2x + x - 1 46. f(x) = 3x – 2x2 + x + 4 47. f(x) = x - 5x² – 11x + 11 %3D 48. f(x) = 2r – x² – 11x – 6 49. f(x) = x' + 3x³ – 5x² + 9 50. f(x) = 4x' – 12x + 27x2 – 54x + 81

Q: 11. What is the general solution of (2a-y)dx + (4x +y-6)dy 0 (a + y- 3) = c(2a+y-4)2 (x - y + 3) =…

A: Given differential equation is                                           (2x-y)dx+(4x+y-6)dy=0 let…

Q: 1) Use reduction of order method with y₁ (x) = e-2x to find a second solution y2 for the DE: y" - 4y…

A: Solution :-

Q: 12. A particular solution of y"– 2y'-8y = (x2+2)e-2 +4xe4z will have the form %3D = (Cx² + Dx +…

A:

Q: 2x4 +3x2 – 1 Rewrite dx as integral of sum of partial fractions. (x³ – 4x² + 5x) B + x-5 C E dx (x +…

A:

Q: B. In each of Problems 4 and 5, eliminate the arbitrary constant using the method you're comfortable…

A:

Q: Find the particular solution of the initial value problem, 4y" – 4y' – 3y = 0,y(0) = 1 and y'(0) = 5…

A:

Q: 12.1 12.2: Problem 3 5 | f(x) dx = 3 and g(x) dx = –4, what is the value If -3

A: Given that: ∫45f(x)dx=3 and ∫-30g(x)dx=-4

Q: 3) Find the particular solution of the DE y" = 12x² if y(0) = 1 and y'(0) = 2.

A: This is a problem related to differential equation. Please follow the procedure given below.

Q: Do you think that the initial-value problem y'=xy^(1/2), y(0)=0 has a unique solution? Justify your…

A: It has no unique solution.

Q: 20) Solve the higher order initial-value problem y"=x+1/x;y(2) =1 and y '(2) = 0 1 7 7 1 15 + -- X-…

A:

Q: 2x4 +3x2 – 1 Rewrite dx as integral of sum of partial fractions. (x³ – 4x² + 5x)? - B + E |dx x+1'…

A: we can reduce into partial fraction

Q: 2. Solve the initial-value problem y"(x)+ 4y'(x) + 6y(x) = x², %3D y(0) = 0, y'(0) = 0. %3D

A:

Q: 6. Solve the initial value problem (2y3 – x³)dx + 3xy?dy = 0, y(1) = 1 a. 5y3x? = x5 + 4 c. 5y3x? =…

A:

Q: X+4 ax 5. S x-3x+2x -dx (by partial fractions) 6. S xV4-8x*

A:

Q: Solve the initial value problem: (x + 2) y' = xy + 2y - 3x - 6 When x=0, y=1

A:

Q: Solve the followina problems: 2. Find the critical numbers of y =2x2 – x4

A: Given, The expression y=2x2-x4 We have to find the critical numbers of the expression.

Q: 1. S 4x-5 dx - partial fraction 2x2 +4x-6

A:

Q: .1) The general solution of the equation y" + y =-5e- , is: - y(x) = Ce-* + ez(Acosx + Bsinx) -e-* O…

A:

Q: Solve the initial value problem. x2у" - 4хy' - бу%3D 0, у(1) %3D з, у'(1) %3D 4

A:

Q: (x-2)²(x³-4) y = Vx2+1 dy If then equals to : dx O y [2/(x-2)+(3x^2)/(x^3-4)-2x/(3x^2+3)] O…

A: The formulas which are used to solve the above problem are stated with the solution.

Q: Find the general solution of y" – 3y' + 2y 1+e-x°

A:

Q: Find the general solution of (xy + 4x)y = 5y² + 4xy². a) Oy + 12y- = -5 In |x| – 16x + C b) Oy - 4y-…

A: First order non linear ordinary differential equation.

Q: How do i get the initial value problem xy’ + 8y = x^6 and y( 1) = 5.

A: Given,                   xy'+8y=x6                    ...(1) and                         y(1)=5.

Q: What is the solution to the initial – value problem : y" = x³ – 1 with y(0) = 8 and y'(0) = 0 ? y =…

A:

Q: Solve the following LP problem using the two-phase method max z= X1 +3x2 subject to X1+ x223 X1…

A: The given problem is Max Z =   x1 + 3 x2subject tox1 +  x2 ≥ 3x1 -  x2 ≥ 1x1 + 2 x2 ≤ 0and x1,x2≥0;…

Q: х4—х2+1 - [3] S [3] s e*ve*-1dx еx+3

A:

Q: 1. Find the particular solution of the DE: y' (x^3) + e^(10x) + 7 if y = 20.1 when x = 0. You may…

A:

Q: What is the solution to the initial – value problem : 4x²y" + 4xy' – y = 0 with y(4) = 2 and y'(4) =…

A:

Q: Find the general solution of dy/dx = (x - 4) / (6 - 5x + x^2). O y = 2 In(x - 2) - In (x - 3) + C y…

A:

Q: What is the value of m if y=mx<-2x-3 has a critical point at x=-2?

A: Given y=mx2-2x-3

Q: 1. y" - 2y' - 3y = e* by D- operator method

A: Since you have posted multiple questions so according to our guidelines we will solve only first…

Q: x2+3 hence evaluate S x2 +3 7. Express in partial fractions x(x2 +1)' dx, leaving your answer in…

A:

Q: Solve using Two Phase Method Max Z = 4x1 + 6x2 Subject to 2x1 + x2 > 4 x1 + 3x2 ≥ 4 x1 + x2 ≤ 5 and…

A: As per the question we are given an linear optimization problem and we have to use the Twl Phase…

Q: 3. Solve the following using Two Phase Method MIN Z = x1 + x2 subject to 2x1 + x2 >= 4 x1 + 7x2 >= 7…

A:

Q: Solve the following problem using the two phase method. min: z = 3x1 + 4x2 -X3 Subject to 3x1 + 2x2…

A: Since there are multiple questions posted the first question is answered.Kindly re post if any…

Q: x³ +x² + x + 3 dx. J (x² + 1)(x² + 3)

A: Given,           ∫x3+x2+x+3x2+1x2+3dx

Q: 4. Solve the IVP y' = 2x-3y +e¯* y'= 2x- 3 y +e * with y(0) = 1 y(0)= 1

A:

Q: In this case, system (1.8) is expressed as (af (Xn-1)+bf (*n-2)), Yn+1 = f (af (yn-1)+bf (yn-2)),…

A:

Q: 2). Solve the initial value problem x2= vx-4, x22, y(2) = 0.

A: From the given problem: xdydx=x2-4 So, we can also write as: dy=x2-4xdx∫dy=∫x2-4xdxy=∫x2-4xdx+C...1…

Q: Solve the higher order initial-value problem f''(x) = x-1/x + 3 ; f'(1) = 3, f(1) = 0

A:

Q: -2 < x < 0, 0 <x < 2; Problem 1: f(x) = f(x +4) = f(x) %3D |2x-,

A: It is known that the general form of Fourier transform is, F(ω)=12π∫-∞+∞f(x)·e-Jωxdx

Q: 2y – x = 3t y + x' = 3e-t ¤ (0) = y (0) = 0 3(s-1) L (x) s2(s+1)(2s²+1) 3(2s-s-1) s2 (s+1)(2s²+1) L…

A:

Q: 2x4 + 3x2 – 1 Rewrite dx as integral of sum of partial fractions. (x³ – 4x² + 5x)? C(2x- 4) +D E(2x…

A:

Q: Solve the initial value problem y'=x^2-4x+3-6e^x, y(0)=8

A:

Q: Use the method of undetermined coefficients to solve the initial value problem x''+4x=3cos2t  ;…

A:

Q: 2x4 + 3x² – 1 (x² – 4x² +5x)? B(2x- 4) + C Rewrite dx as integral of sum of partial fraction D(2x-…

A: Here we have to apply partial fraction.

Q: What is the solution to the initial – value problem : x²y" + xy' – y = 0 with y(1) = 2 and y'(1) = 4…

A:

Q: Solve the initial value problem xy‘ + 2y = 3x, y(2) = 3 for y = y(x).

A:

Q: Solve the general solution of the given DE * dy = (-5x + y)² – 4 dx 3 (1+ ce6x ) 3 (1 – ce6*) y = 5x…

A:

Q: Find the equilibrium point for a product D(x)=16-.004X^2 and s(x)=.005X^2. Round only final answers…

A:

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.