Use Galerkin's method to formulate a linear finite element for solving the differential equation d'y dy - 4x = 0 dx dx? subject to y(1) = y(2) = 0.

Q: dy + у 1-y %3D ху dx

A: Here I am attaching image so that you understand each and every step.

Q: If the characteristic equation of the differential equation dy dy + y = 0 has two equal + 20 dx2 dx…

A: Quadratic Equation: A quadratic equation is an equation of degree 2. The standard form of a…

Q: The integrating factor for the differential equation (xy³)dx + (x²y² + 1)dy = 0 is

A:

Q: Consider the differential equation (xy + x)dx = (x²y² – x² + y² – 1) dy. By separation of variables,…

A:

Q: Find the integrating factor of the non-exact differential equation: dy= (e2x+y-1) dx

A: Given differential equation is dy=e2x+y-1dx which can also be written as e2x+y-1dx-dy=0 Comparing…

Q: Find the general solution of the second order differential equation below: dx d) dt2 + 6x = 0 dt

A:

Q: dy dx

A:

Q: The integrating factor for the differential equation (3xy + y)dx + (x2 + xy)dy 0 is - X Y O - Y O

A:

Q: Find the solution of the differential equation that satisfies the given inital condition.…

A:

Q: Find the solution of the differential equation that satisfiesthe given initial condition.

A: The given differential equation can be solved by the variable separable method. first, separate the…

Q: In the autonomous differential equation dx = x²(1 – x), dt

A:

Q: solve the differential equation dy/dx=2x^4sqrt of y, y.0

A: Solution of given question is written in below steps.

Q: Find the general solution for differential equation.

A: To obtain the solution of the differential equation dydx=4e2x, multiple both sides by dx and then…

Q: Solve the differential equation dy/dx =x/y2 with initial condition y(0) = 2.

A: Given : dydx = xy2

Q: Find the general solution of the ordinary differential equation: r²y" – ry + y %3D

A: The differential equation is given as x2y''-xy'+y=2x                         (1) It is a Cauchy…

Q: Find the solution to the differential equation dz/dt=7te^(5z) that passes through the origin.

A:

Q: The solution of the separable differential equation = (1+y²)x is: %3D dx

A:

Q: What is the linear differential equation of dy/dx+2xy+xy^4=0 using dv/dx?

A:

Q: 3. Plot the slope field for the differential equation = y² – x and sketch the solution for the…

A: Given: A differential equation dydx=y2-x. To sketch: Slope field of given differential equation and…

Q: find the solution of differential equation 1 + x dy + dx y =

A: we have to find the solution of differential equation: dydx+1+xxy=exx

Q: Calculate the solution to the differential equation dy = 2e- with y(0) = 1. dz

A:

Q: Find the linear differential equation of the bernoulli’s equation dy/dx-y[1/(2x)]-y^5=0 using dv/dx.

A:

Q: Find the general solution of the first-order linear differential equation. dy dx x² x > 0 y =

A:

Q: dx at + tx + = 0

A:

Q: Find the general solution of the differential equation: 3ydx = (3x + 1)dy

A:

Q: Find the integrating factor of the non-exact differential equation : (3x²y+6xy+y³) dx+3(x²+y²) dy=0

A: Given a differential equation, 3x2y+6xy+y3dx+3x2+y2dy=0. To find the integrating factor of the given…

Q: (D – 3D + 2) y = (1+ e-")?

A: I am attaching image so that you understand each and every step.

Q: Find the solution of the differential equation that satisfies the given initial condition. dy y(0) =…

A:

Q: The integrating factor of the differential equation 2xy dx + (4y + 3x^2) dy = 0 is . Does not exist

A: Ist question was incomplete I have to do the second question Please repost ist question correctly

Q: Solve the differential equation (y+xy+ 1) dx + (x²+xy²+2y) dy=0 by forming integrable combinations.

A:

Q: Solve the partial differential equation xp+yq=z.

A: According to the lagrange linear equation, Pp+Qq=R the solution is,

Q: Consider the autonomous differential equation, without solving, sketch what the solution curve would…

A:

Q: Show that y is a solution of differential equation = 1-. dy %3D dx

A: y'(x)=1-yx We can simplify it as: dydx+yx=1First-order linear ordinary differential equation.…

Q: Find the general solution of the first-order linear differential equation. +3y=6 dx

A: Let the given differential equation is: dydx+Py=Q where P and Q are functions of x (or constants)…

Q: solve the differential equation using Bernoulli. xydx+(x2-3y)dy=0

A: Given differential equation is  xydx+x2-3ydy=0 which can be written as…

Q: Show that In y | In x dy = 0 dx +|1+ is an exact differential equation. Hence, find the solution.

A: The given differential equation is                                                         1+ln…

Q: Use the method of undetermined coefficients to find a general solution to the differential equation:…

A:

Q: Write down a differential equation of the form = ay+b where all solutions approach y = dt as t → 0.

A: The given question is solved below.

Q: dy 2y2 + x²e=(÷)² dx 2xy

A: dydx=2y2+x2e-yx22xy----(i)Let y = xudydx=xdydx+uPut the value of y and dydx in equation (i) we get…

Q: An integrating factor for the linear differential equation Y' - 2y = 12x is l=

A: The given differential equation is y'-2y=12x. Clearly, the given DE is a first order linear…

Q: Discretize the differential equation y" – y' + 4ty = 5(t + ), y'(-2) = 0. y'(1) = 0 with step-size h…

A: Using center difference method, we can approximate y' and y" as follows.…

Q: Solve the differential equation dy/dx=5-x/y with the inital condition y(6)=-4.

A: We have to solve

Q: Find the particular solution of the differential equation that satisfies the initial condition.…

A:

Q: Find the general solution of the differential equation - 3y = x*cosx. dx dy osx. -

A:

Q: Calculate the particular solution to the forced differential equation x" + 3x = 5cos(2t)

A:

Q: . The standard form of the first order linear differential equation x y'+xy +2 = 0 is,

A: This question is based on to form a standard first order differential equation.

Q: Use the initial condition to find the particular solution of the differential equation. Differential…

A: In this question, separate y terms in LHS and x terms in RHS and then integrate both sides to get…

Q: What is the particular solution to the dy dx a°+3 with the 3y differential equation initial…

A: The differential equation dydx=x2+33y is separable because it's the form of dydx=f(x)g(y) where…

Q: 2(2x? + у?)dx — ху dy %3D 0

A:

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.