8. Derive the recursive formula for the numerical solution of the following differential equation: x(t)= - 5x(t)+u(t), where u(t)=1(t) and the step size is h=0.1. 8.a. for the explicit Euler method. 8.b. for the improved Euler method.

Q: Find the general solution of the following differential equation. y" + 4y + 8y = 0 NOTE: Use c₁ and…

A:

Q: Find the general solution of the given linear differential equations y" - y = cos x - 5 sin(2x) By:…

A: 1) By using method of undetermined coefficient ,  We have given a differential equation  ,  y'' - y…

Q: find the general solution to the given differential equation on the interval (0,∞). Q. x2y′′+9xy′+16y…

A:

Q: Equalions 1. Find the explicit particular solution of the differential equation for the initial…

A:

Q: as instructed, to find a second solution y₂(x). I x²y" - xy' + 10y = 0; Y₁ = x cos(3 In(x))

A:

Q: Determine the value at x =

A: Given,              y'=e-y2x-5, x=2.4and initial value of y(0)=2.

Q: 7) A building is 300 feet tall. It casts a 165 foot long shadow. A statue near the building is 40…

A: Given: A building is 300 feet tall. It casts a 165 foot long shadow. A statue near the building is…

Q: Q2j Solve the following differential equations. dx dx = 3. Find Y using D-operator, where Yp (D+1)…

A:

Q: 1. (2xy² + ye*)dx + (2x²y + ke* – 1)dy = 0 2. (6xy³ + cos y) dx + (kx²y² – x sin y) dy = 0 %3D

A:

Q: 5. Verify that the functions e, xe: form a fundamental set of solutions of the DE 4y" – 4y'+y = 0 on…

A: We have to general solution of given differential equation and show that given set of solutions are…

Q: 1. Find a value of p for which the following differential equation becomes exact. Hence solve the…

A: (3x2y-xy2)dx+(px3-x2y)dy=0it is of the form Mdx+Ndy=0whereM=(3x2y-xy2)N=(px3-x2y)The given equation…

Q: Solve the differential equation using Variation of Parameters et (D² – 2D + 1)y

A:

Q: Find the general solution of the following differential equation. y" + 2y + 5y = 0 NOTE: Use c₁ and…

A:

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

A:

Q: Find the general solution of the following differential equation. y" + 4y - 12y = 0 NOTE: Use c₁ and…

A:

Q: 2x/nx. 6) x?yll+ xy's dy= %3D

A:

Q: Solve the differential equation. dy dx = 6x√/25-y², -5<y<5 The solution is (Type an equation.) ***

A: The solution is given below:

Q: Solve the following differential equations properly 7. (x2 + 4)3/2dy+ (y²/y² – 4 )dx = 0

A:

Q: (2x – y)dx + (4 + y – 6)dy = 0 - -

A:

Q: (b) The following ordinary differential equation is given, where y = y(x) y' - xy2 = 0 At x = 0,…

A: For solving this question, the following formulae and notations are used: Given an ordinary…

Q: Solve the following differential equation: (sen(y) — ysen(x)) dx + (cos(x) + хcos(у) — у) dy %3D 0

A:

Q: 3 3 Find the general solution of (2y) dx + (x – x’y°) dy = 0. A. x'y3 – 2 = Cx?y В. хуз + 2 %3D Сх'у…

A:

Q: Find the general solution of the following differential equation. Primes denote derivatives with…

A:

Q: DETAILS ZILLDIFFEQMODAP11 4.2.009.EP. The indicated function y(x) is a solution of the given…

A: