Consider the equation 2y 32(8x² - y) dx + x x) dy 16x dy = 0. Find an integrating factor u(x) (so a function of x alone). u(x) = help (formulas) Now once you have an integrating factor, you can solve the equation as an exact equation. An explicit solution can be found, that is, one of the form y = y(x). Find an explicit solution that solves y(1) = 5. y(x) = ☐ help (formulas) Book: Section 1.8 of Notes on Diffy Qs

Q: Find the solution of the given initial value problem in explicit form. () T sin(2x) dx + cos(9y) dy…

A:

Q: How could the 1D heat equation represent physically?

A: We know that the heat energy of a body with uniform property is represented as; where c is the…

Q: Solve: x'y" - 7xy' + 41y =0

A:

Q: Solve 4xx = ut + tx u(x, 0) = 0

A: The provided partial differential equation (PDE) describes a transport phenomenon represented by the…

Q: Find the general solution by undetermined coefficients.  y'' + y = 2x2e-x.

A:

Q: Jx -Jx-15 = 3 JX-15 =Jx - 3 X-15= Salvethe equation

A:

Q: Determine all solutions. y'= (x-y + 3)²

A:

Q: Determine the differential of y for the function y=3ln(4x2).  Simplify fully.

A: To Determine: Differential of y

Q: The general solution of y' x2 can be written in the form

A:

Q: B. Find the first and second derivatives of i- y =-10x+3cosx+(2x+3)(5x-4x) 5x+1 ii- y= 2x

A:

Q: 2) Solve the equation y' = Y 4x²y + x

A:

Q: 2. Solve x². dy + 2xy = 4x³ using an + 2xy = 4x³ using an Integrating Factor. dx

A:

Q: Solve for ‘x’ and ‘y’ where x + y = a – b, ax – by = a2 + b2

A: To solve the equation for x and y.

Q: у %3D V1+ 2х (1 — х)-3

A:

Q: If u(x) = x3, then du = 3x2.

A:

Q: Solve dy/dx + 2y = 4, y(0) = 3 by one of the usual methods. Solve same the problem by Picard’s…

A: Integrating factor method for solving a differtial equation  Consider the differtial equation…