Differential Equations Answers

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=te^2t

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

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

1. D’après la méthode des différences finies, quel est le schéma avancé de la dérivée première, seconde et troisième avec une précision du second ordre ?
2. Soit l'équation suivante:

d³y/dt³+2d²y/dt²+4dy/dt+8y=te²t

avec y(0) = 0 et y(3) = 28.2

En utilisant les resultats de la partie (1); résoudre l'équation pour t appartenant à [0 ; 3] avec le delta t = 0,3.