Q3- Solve the following initial value problem over the interval from x = 2.5 to x = 3.5 with a step size of 0.25 and initial value of y(2.5) = 3.27388. Solve the problem using Huen's %3D method. dy = -0.5y + e-* dx

Q: 2 3/2 between x = 0 and x = 1 is 3 %3D The length of the curve y =

A: We will find out the length of curve.

Q: d²y Solve the particular solution for = 2 – 4x when points (0, 2) and (-1, 3) are on the dx2 curve.

A:

Q: Suppose that x and y represent the amounts of two basic inputs for a production process and…

A: Suppose that x and y represent the amounts of two basic inputs for a production process   The…

Q: Find dy/dx for each of the following. Do not simplify your answers. 3 (a) y = 3* – 3x7 + cot(3x³ +…

A: Part(a) Given

Q: (a) Find an approximate value of S x*e*dx (b) Solve for -dx x²+9 xp

A: Here we have to find the value of given definite integral.

Q: Solve for y: O y = Oy = x = 4ln(y - 8). 1 4 ln(x - 8) x+8 4 O y = e-4x + 8 O y = 4 ln(x - 8) Oy =…

A:

Q: Solve the equation dy, 3y + dx +2 = 3x, y(1) = 1.

A:

Q: x² -4 f(x) = x² - 5x+6 find asymbtotes

A: There are 3 types of asymptotes

Q: Solve the following; (a) e2-3z = 6 (b) In(2. + 5) = 4 2 dr %3D %3D

A: (a) Given equation is: e2-3x=6 To find the value of x.

Q: y = (ax-1) (6x.+5]%3 find dy dx 10

A:

Q: Q2: find y' y= 33xelnx²

A: We have the given function : y=33xelnx2 We have to find the derivative of this function.

Q: Calculate dy/dx. You need not expand your answer. y =x2.3/9+2/x2.3)(9x − 1) Answer ----->dy/dx:…

A:

Q: x (х+1) dw solve for dx W 2х-1

A: The Quotient rule: fg'=f'·g-g'·fg2 The product rule: f·g'=f'·g+f·g' Given: w=xx+12x-1

Q: 3. x² - x dx =? %3D [x-1]

A:

Q: y = √sin(7x + In(5x))

A: We know that the derivative of x^n=nx^(n-1) So derivative of sqrtx=1/(2sqrtx)

Q: 22. y = sec 4(4+x³) 5

A:

Q: A linear model of the spread of an epidemic in a community of 1000 people is the equation: dx/dt =…

A: To find the number of people x(t) who have contracted the disease at the time oftime t.

Q: (b) Solve the equation 2 = dy %3D -x+/x²+yz y(-3) = 4 for -3 <x57 taking the dx y step-length h =…

A:

Q: y' = e2x + y – 1

A: Using method of linear differential equation.

Q: 3. Solve the following: 2xdx (x²+1)2 a. b. y = f xe* dx, given y=0 when x=0 x-2x+1 dx с. d. sn (Inx)…

A: According to our guidelines we can answer only first three sub-parts and rest can be reposted.

Q: Q2: find y' y= 33xelnx?

A: Use the product rule, ddx(f.g)=f.ddx(g)+ddx(f).g Use the derivatives, ddx(ax)=axloga…

Q: dy Solve = dx 2-y 2-x

A: To solve the given differential equation

Q: Solve and sketch the graph of the IVP. dy dt = 81 (1)-82(1) +83 (1)-84(1)+.... y(0) = 0

A: As per the question we are given the following IVP : differential equation(DE) : dy/dt = δ1(t) -…