Solve the differential equation by variation of parameters. y" + 3y + 2y = = 1 2 + ex

Q: Use the greedy algorithm to make change using quarters, dimes, nickels, and pennies for 5100 rupees

A: It is known that 1 quarter = 25 cents, 1 dime = 10 cents, 1 nickel = 5 cents, 1 penny = 1cent. Also,…

Q: The quantity of the demand per month of a certain accessory is related to the price (in 500 0.01x²…

A: Given that the demand function is Px=5000.01x2+1. We have to find the number of accessories must be…

Q: Find the area between y = √x + 5 and Y graph. If needed, round your answer to 2 decimal places. -7…

A:

Q: Solve the differential equation by variation of parameters. 1 6 + ex y" + 3y' + 2y =

A: y''+3y'+2y=16+ex we have to solver above differential equation using variation of parameters.

Q: Consider the IVP +20² dt² dx dt 4t- + 4x = 0, with x(1) = 0 and x' (1) = -3. Show that x₁(t) = t and…

A:

Q: An experiment was conducted in order to determine if cerebral blood flow in human beings can be…

A: We need to fit the given dataset into a quadratic equation of the form: y=a+bx+cx2 and then…

Q: Find a function u(x, y) which satisfies the Laplace equation 1 = Urr + = U₁ + 7/124606 = 0 Au in the…

A: As per the question we are given the Laplace equation  ∆u = 0 in polar coordinates. And the domain…

Q: In the following exercises, find the Jacobian J of the transformation.

A: Introduction: A partial derivative matrix is a jacobian matrix. Jacobian is the determinant of the…

Q: Prove the following by mathematical induction. V4 ≤NEN, 2n<n!.

A: We have to prove ∀ 4⩽n∈ℕ,  2n&lt;n! using mathematical induction.

Q: Determine whether the given set of functions is linearly dependent or linearly independent on the…

A: The given set of functions                                    f1(x)=cos2x, f2x=1, f3x=cos2x We have…

Q: calculation for P.I ур cos²x b²+1 2 cos²x D² + 1 + {² 22{ -} 1+ cos2x D² + 1 HOW DID HE GET THE…

A: The particular integral is solved as  yp=1D2+1(cos2x)

Q: In the following exercises, evaluate the triple integrals over the bounded (egion where f(xy +…

A:

Q: nd a linear differential operator that annihilates the given function. (Use D for the differential…

A:

Q: 22. Evaluate without using a calculator. log 0.00001 log, 729 1 64 a) b) c) log₂

A: The given problem is to evaluate and simplify the given logarithmic expressions.

Q: b) Given the following operation 4.232 +2.0321 +5.43 -2.38 Compute the most accurate value for the…

A:

Q: Find the area of the plane z = 4x + y for all (x, y) = R where Ris the region in the first quadrant…

A: Consider the equation of the plane, z=4x+y for all x,y∈R,where R is the region in first quadrant…

Q: The indicated function y₁(x) is a solution of the given differential equation. Use reduction of…

A:

Q: The indicated function y(x) is a solution of the given differential equation. Use reduction of order…

A:

Q: a) Find the values A and B that allow the vector field given below to be conserved. F(x,y,z)=2xlnz…

A: (a) Given vector field is Fx,y,z=2xlnz i+3Bz j+x2zA+y3k Now, F1=2xlnzF2=3Bz F3=x2zA+y3

Q: 8. Consider the solutions Y (t) of Y'(t) + aY(t) = de-bt with a, b, d constants and a, b > 0.…

A: We find solution for the both cases.

Q: The given family of functions is the general solution of the differential equation on the indicated…

A: Given : y" -y =0 y=c1ex +c2e-x y0 =0y'0 =5    find : y

Q: Let f₁(x) = x² and f₂(x) = x³. Complete the Wronskian for these functions. |x² w(x², x5)= 2x

A: Wronskian is a deteminant which is test for proving whether solutions are linearly independent or…

Q: A force of 640 newtons stretches a spring 4 meters. A mass of 40 kilograms is attached to the end of…

A: Given that a mass of 40 kilograms is attached to the end of the spring and is initially released…

Q: a) Given the curve y = f(x) as in Figure 1. y i. ii. iii. 3 2 -1- 0 1 f(x) = 2 (3 + x) (1+x²) 3…

A: As per our company guideline we are supposed to answer only first  qs, kindly post remaining qs in…

Q: 2 Solve the following ODES by Inverse Operator method ● 2 (B²+1) y = cos x Ans & Y = C₁ C3 x + C₂…

A:

Q: (a) Let B = {V₁, V2, ..., Vn} be a basis for a finite-dimensional vector space V. Prove that for…

A:

Q: Find a linear differential operator that annihilates the given function. (Use D for the different…

A: The annihilator of xn-1 is Dn The annihilator of xn-1sin βx is D2+β2n Now the given function is…

Q: Find the solution of the given initial value problem. 6y""+24y' 480y = 0; y(0) = 11, y'(0) = 10,…

A: given initial value problem 6y'''+24y'-480y=0 y(0)=11, y'(0)=10, y''(0)=-156 We have to find its…

Q: calculation for P.I ур cos² D²+1 cos²x 2 { 2005x } D² + 1 y = 1+ cos2x D² + 1 HOW DID HE GET THE…

A: We are just multiplying and dividing by 2 on the right hand side.

Q: 382. x = u cos(e"), y = u sin(e")

A: 382 Given that x=ucosev and y=usinev. We have to find the Jacobian J. The Jacobian J is given by…

Q: In the following exercises, change the order of integration by integrating first with respect to z,…

A:

Q: the function f (x, y) = xy2 +1/6 x3 − X + 1 is given. a) find and classify all critical points of…

A: Let us consider the given function f(x,y). Determine the critical points. Find the partial…

Q: • (D² - 1) y = sinx -X Anse y=c₁e +₂e + c3 cosx + cusinx + = (e + e + cosx) 4 = 2 sinhx +

A:

Q: The indicated function y₁(x) is a solution of the given differential equation. Use reduction of…

A:

Q: Determine whether the given set of f₁(x) = x, f₂(x) = x= 1, O linearly dependent O linearly…

A: I have given the answer in the next step. Hope you understand that

Q: Which of the following functions would translate the given function horizontally 4 unit to the left:…

A: We Know that, The function notation, to shift a function horizontally to left, add inside the…

Q: Use the divergence of the vector field to compute F(x, y) У · (tan-¹ (2x))i + (xy − 2 + 8x²) j - = 4…

A: we are given the vector field as  F(x,y)=tan-1(2x)4i+(xy-y2+8x2)j to compute…

Q: The given family of functions is the general solution of the differential equation on the indicated…

A:

Q: Find a homogeneous linear differential equation with constant coefficients whose general solution is…

A: Given equation: y = c1 + c2x + c3e3x Now, differentiating w.r.t "x" y' =  c2+ 3c3e3x (here c1, c2,…

Q: (a) F(s) = 2s (s¹ +24s² +144)

A: Since you have asked multiple questions here, we will solve the first question for you. To get the…

Q: Based on data given in table 1: k Xk Ук 0 2 1.5 Table 1 1 4 3.0 2 6 4.0 Estimate the following: a)…

A:

Q: Question 26 Calculate the average rate of change for the function f(x) = 2x² − 3x + 5 1 over the…

A:

Q: Find the determinant. -K² = (x²)(3x²) - (2x) (x³) w(x³, x²) = The Wronskian is not is not equal to 0…

A:

Q: State the domain and range of the following function: ƒ(x) = ²log((−4(x − 12)) + 3 domain {x € R/x…

A: Domain and range of the function

Q: Question 17 Solve the following trigonometric equation for 0 ≤0 ≤ 27. Show your work. 2 4 sin²x-1=0

A: Use the given information.

Q: compute the partial sum when k=1 goes until infinity of ak. ak = 1/((k^2)+3k+2)

A:

Q: f(x) transformations, proper order, at are - 8 log x + 6 into f(x) = = 4 log x + 1 the followin…

A: given function f(x)=-8logx+6 we have to transform into f(x)=4logx+1 Remember the following…

Q: sider the Set Q of rational numbers, and let =a+b-ab. Then (Q,*) is a ect one: a. semigroup b. none…

A:

Q: Find the general solution of the given second-order differential equation. 3y" + y = 0 y(x) = ||

A: We have to find the general solution of given second order differential equation

Q: a) Given the curve y = f(x) as in Figure 1. y i. ii. iii. 3 N -1- lo 0 f(x) = 2 (3+x) (1+x²) 3…

A: "Since you have asked multiple questions, we will solve the first question for you. If you want any…