As a special case in which the error of Euler's method can be analyzed directly, consider Euler's method applied to Y'(t) = Y (t), Y(0) = 1. %3D

Q: Derive the formula of the P/G factor : (1+i)" - 1 1 (P/G, i,n) = %31 i(1+i)" (1+i)"

A: We will follow given steps to find out the P/G factor. First, we start with writing…

Q: If f(x) = sin x 7T find f %3D (a) 1 (b) / 2 2. . т (c) 1– 4 (d) V2 1+ (e) /2 (1- 3)

A:

Q: If f(x) = xe , x >0 and (Y = ln(X)), then the PDF of Y is %3D (In(1)² (In(y))e ye

A: Answer: ⊙ ey-12e2y

Q: Find the derivative of f(x) = log, (x° + x – 1). %3D 2 + x - 1 f (2) = %3D (3z* + 1) (In 2) (3z +1)…

A: Given:     fx=log2x3+x-1

Q: If g(x) = xsin(x), then what is g'(2)? Round to the nearest hundredth.

A: Find out g’(2) Take first derivative for g(x) by applying product rule

Q: In this question, we are going to estimate the value of (6/5)^1/3 without a calculator, with the…

A:

Q: find y' (xy)x = e

A: Given problem:- find y'   (xy)x = e

Q: Show that Costy+ Co5' (-x ) = TT.

A: To show that the given identity is true,

Q: Identify f(x) to be used in variation of parameters to solve for y, e" y" + y' – 3y = x

A: To find f(x) write equation in form of y" + P y' +Q y = f(x).

Q: Compute the second derivative of f(x)=ex+x at x = 1 using a step size h = 0.2

A: To find the second derivative of f at x = 1. The approximation formula for second derivative at a…

Q: Holli O’Leary sells copy machines. She carries 3 models.  Price and monthly sales for each model are…

A: Model Price Number sold Workmaster $500 47 Auto-Feed $850 22 Deluxe $2300 8

Q: If g'(x) = Vx -+ Vĩ, g(0) = 2, then g(1) = ? %3D %3D Answer:

A: Topic- integration

Q: From Variation of parameters for the 2 -1 X' X + e 3 -2

A:

Q: Take first and second derivatives of y = xr, y=(ax2 + bx + c)2, y=ecx, y=e-cx, y=ln(x).  In all…

A:

Q: (10) Solve the given BVP by using Green's function: ; (ii) y" – y/ = e2; y(0) = 0, y(1) = 0

A: Given differential equation is: y''-y'=e2x y(0)=0y(1)=0 Green function in equation is given by:…

Q: Solve y" - y' = xe characteristic equation using undetermined coefficient. Show all your work. The 2…

A: To solve the differential equation y''-y'=xex using undetermined coefficients.

Q: If P(A')= 0.4 and P( A and B)= 0.30, then find P(B|A)?

A: Answer: From the given data, P(A') = 0.4 Since, P(A) + P(A') = 1 P(A) = 1 - P(A') = 1 - 0.4 = 0.6…

Q: If y = (3x+8)x, compute y'(1). y'(1) = X

A: We know that; The Power law: ddxxn=nxn-1 The Chain rule: fgx'=f'gx·g'x The Product rule:…

Q: Use any method to find the GS of (+ Inx) y' + ( + y) = ln = 0 y

A:

Q: If h(x) = f(x) – g°(x), f'(x) = -9(x) and g'(x) = f(x), then h'(x) is: %3D

A: The solution of the problem is given in the next step.

Q: If g(x) = f(x² + 9x) and f'(10) = 3 , %3D %3D then g'(1) = (A) 11 (B) 3 (C) 33 (D) 29 (E) 87 (A) (B)

A:

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.