Consider the nonhomogeneous equation: y" + by' + y = g(æ) %3D where b is a real constant. The following questions refer to your guess for Yp using the method of undetermined coefficients. Do not solve for the coefficients. (a) If g(x) = 3x – 1, what is the first guess for y,? (b) Identify the value of b if g(x) = 7 sin x and you need your second guess for Yp. What is that guess? (c) Identify the value of b if g(x) = 18e" and you need your third guess for Yp. What is that guess? (d) Explain why you will never need more than three guesses.

Q: Solve the following equation: xy' + y = − 2x6y¹

A: Given differential equation isxy′+y=−2x6y4Rewrite this equation asy′y4+1x1y3=−2x5Substituting,…

Q: 2. fn (x) = -nx² E (-∞, +∞). Hint: find sup | fn (x)|. = nxe

A:

Q: Solve (sin(x) cos(y)) dx + (cos(x) sin(y))dy = 0 if possible. If the equation is not exact, say so.…

A: First we check given differential equation is exact or not.  If given differential equation is exact…

Q: Determine a suitable form for Y (t) if the method of undetermined coefficients is to be used. y(4) +…

A:

Q: I.x''-9x=cos(t) II. x''+9x=cos2(t) III. x''+4x=sin(2t)   Solve equation-(I) using the method of…

A: We are entitled to solve only one question at a time. Given - x'' - 9x = cost To find - Solve…

Q: Given that 7g(x) + 3x sin(g(x)) = 8x? – 50x + 63 and g( ) = 0, find g'().

A:

Q: 1) BASIC DERIVATIVES: Differentiate and simplify the following functions a) f(x) = 5x³+3x² - 5x+2 b)…

A: We know that the derivative of x^n Is  nx^(n-1)

Q: Determine the form yp using undetermined coefficients. Use A, B, C and etc. for constants. No need…

A:

Q: Determine a suitable form for Y(t) if the method of undetermined coefficients is to be used. y (4) +…

A: Introduction: The method of undetermined coefficient is a method to determine the particular…

Q: Problem 3: Find (i) f'(x) and (ii) f"(x) of the following functions. 6x4-√x , c) ƒ(x) = e4 – 5e-5x -…

A: As per the rules of the company we can answer only the first question and rest can be reposted.

Q: How would i find the derivatives of this inverse trig. problem? y = (1+Tan-1x)2

A: Given that the given function is

Q: Use the variation of parameters to solve the given equation: (a) y"+y"-4y'-4y = 2e¯* +4e²x

A:

Q: Find the general solution for the following equation: y' = (2²4) (3y + 2)

A:

Q: 2x If ƒ (x) = e²x (x³ + 1), then ƒ¹ (2) =

A: If , then to determine .

Q: at What point (x,x) ber is closest to the origin ✓= Vio-3x A

A: Y2=10-3x  We have to find the point one the curve which is closest to origin .

Q: Determine a suitable form for Y (t) if the method of undetermined coefficients is to be used. y(4) +…

A:

Q: 1. Placed on the axes below is the graph of S(x)=x' +3x² +2. With the graph, are five rectangles.…

A: f(x)=x3+3x2+2. we have to find area of the rectangles.

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.