Differential Equations Answers

Write the given differential equation in the form L(y) = g(x),

 where L is a linear differential operator with constant coefficients. If possible, factor L. (Use D for the differential operator.)

3y'' − 8y' − 3y = 4

Find a linear differential operator that annihilates the given function. (Use D for the differential operator.)

7x − sin(x) + 20 cos(5x)

U(x+y) U_x + U (x-y) U_y = x² + y²

(x-y)p-(x-y+z)q=z

Find the general integral of the equation

(x-y)p+(y-x-z)q=z,

And the particular solution through the circle z=1,x²+y²=1

Suppose u(x) = cot x is an Integrating factor of the differential equation (sin x)? y" = 2y, find the general solution.

y" - y = e2x[3 tan e+ 3 (sec e*)2]

Solve the pfaffian D.E. y(x+4)(y+z)dx - x(y+3z)dy+2xydz =0

Ydx+(y-x)dy

1) Based on the finite difference method, what is the advanced scheme of the first, second and third derivatives with second order accuracy?

2) Consider the following equation:

d³y/dt³+2d²y/dt²+4dy/dt+8y=te²t

Where y(0) = 0 and y(3) = 28.2

By using the results from the session (1), solve the equation for t E [0 ; 3], with delta(t) = 0.3