### Linear Differential Equations - Finding a Particular Solution

Calculate the unique solution for 7e^x in the following non-homogeneous second-order linear equation, showing all the steps. d²y/dx² + 5dy/dx - 6y = 7e^x

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Calculate the unique solution for 7e^x in the following non-homogeneous second-order linear equation, showing all the steps. d²y/dx² + 5dy/dx - 6y = 7e^x

Please find the particular solution for xe^x in this problem and show all details. d²y/dx² - y = xe^x

The hemisphere is given by f (x,y) = sqrt 64 - x^2 - y^2. Sketch a contour map for this surface using the level curves corresponding to c = 0,1,2,3,4,5,6,7,8 Since this is an example shown in the book, I can see that when c = 8 you draw a circle with a radius of 8 and when c = 0 you have a point at the center of the circle.

The differential equation is: d²y/dx² - y = xe^x For the first part of the general solution, I got y=Ae^x + Be^-x where a and b are constants. Now I need to find the particular solution. Thanks.

Please see the attached file for the fully formatted problems. Please do problems 3 - 8, 10, 12, 14, 16 - 40 even, 42 ,44,45-49, 54 - 60 odd.

Please find the general solution of the nonhomogenous second order linear differential equation below by following these steps: 1. Find the general solution y= C1y1 + C2y2 of the associated homogenous equation (complementary solution) 2. Find a single solution of yp of above.(particular solution). 3. Express the general so

Find the particular solution of the general equation below, given the initial conditions. Please show all details in the solution, simplifying if possible. Thank you. y=C(e^(-2x))sinx + C(e^(-2x))cos x y(0)= 1 y'(0)= 0

Please find the particular solution of the differential equation below satisfying the given initial conditions. The equation needs to be put in standard form (s² + bs + c = 0). The roots need to be found, and then plugged into the appropriate general formula that satisfies whether b² + 4c is less than, greater than, or equa

Use a graph and level curves to estmate the local maximum and minimum values and saddle points of f(x,y) = x^3 - 3*x + y^4 - 2*y^2; then use calculus techniques to find these values precisely.

At time t = 0 a baseball that is 5 feet above the ground is hit with a bat. The ball leaves the bat with a speed of 80 feet per second at an angle of 30 degrees above horizontal. a) How long will it take for the baseball to hit the ground? b) Use the result in part a to find the horizontal distance traveled by the ball. Ple

1. For a thermodynamic process involving a perfect gas, the intial and final temperatures are related by: where is the specific heat capacity of the gas, is the change of entropy and and are the initial and final temperatures of the process. Determine the value of if and . 2. The overall efficiency of a gas turbi

Find the general solution of the Bernoulli equation: dy/dx -y/x = (y^4 cosx/x^3) A fully charged capacitor is discharged and the current i(t) flowing through a series of RC circuit at time t satisfying the equation: 1540 di/dt +800i =0. Given that E=115 V, draw the complete RC circuit and sketch the current (i) waveform.

Please answer the attached questions. On question #3 the last two mutliple choice options didn't scan they are: c.Yes, the limit exists, and is equal to -1. d. Yes, the limit exists, and is equal to 0.

Suppose and have radii of convergence R1 and R2, respectively, where R1 and R2 are non-zero real numbers. What can be said about the radius of convergence of the following series. Justify youtr answers, ? ? ? ? , where Please see the attached file for the fully formatted problems.

Please solve the following differential equation, showing all steps and substitutions. Thank you. tanθdr/dθ + r = sin²θ

Please solve the differential equation below. Please show all steps. dy/dx=(2x²+1)/(xe^y)

Please solve the differential equation: dy/dx=x²√y, y>0

Please find the initial value of this problem: d³θ/dt³=0; d²θ/dt²= -2; dθ/dt= -½; θ;=√;2 when t=0 Please show all steps. Thank you

I am asked to find the initial value. The given information is: d²y/dx² = 0 dy/dx=2 y=0 when x=0

I need help with the problem! xy' + xy + 2y - 2e^(-x) = 0 I had a hard time figuring out how to solve it... please help!

(1 + x^2 + Y^2 +(x^2)(y^2))dy = (y^2)dx

(y^2 + yx)dx + x(^2)dy=0

Please answer the following questions: The Present value of money is the amount that you need to deposit now in order to have a desired amount sometime in the future . 1. What is the present value needed in order to have saved $60,000 in five years, given an annual interest rate of 7% compounded monthly? 2. What is the

Refer to figure 2 in attachment. a) Write the equations of motion for the mechanical system.****PLEASE SHOW YOUR FREE-BODY FOR EACH MASS****THANKS B) Take the Laplace transform of these equations, arrange them in matrix form, solve for the displacement x2(t), and find the transfer function T(s)= X1(s)/F(s) C) Using the co

The function is given by the formula f(x) = (5x3 + 16x2 + 12x + 27)/(x + 3) when x<-3 and by the formula f(x) = -5x2 - x + a when -3=< x. What value must be chosen for a in order to make this function continuous at -3?

How does a bonds value change with the interest rate?

X'' + 2x' + x = 5exp(-t) + t for t greater/equal to zero; x(0)=2; x'(0)=1 and identify critically damp, over-damped or under-damped (overdamped or underdamped). thank you

Prove the given identity - Please explain in detail. 14. 2 cos x - 2 cos^3x = sin x sin 2x 16. cos (x-y)/cos x cosy = 1 tan x tany 20. sec x -cos x = sin x tanx 22. sin 2x = 1/tanx +cot 2x 23. If tan x = 5/12 and sin x>0 , find sin 2x 26. If sin x = -12/13 with pie <x<3pie/2, and sec y = 13/12 with 3 pi

1. cot²x-cos²x = cos²xcot²x 2. cotx = cscx/secx 3. tanx = sq.rt. sec²x-1 4. sinx/1-cotx + cosx/ 1-tanx = cosx + sin 5. cotx-1/1-tanx = cscx/secx 6. cosxsiny = 1/2 (sin(x+y) - sin (x-y))