Answer to Question #330653 in Differential Equations for Rohit

Question

Solve the following :-

a) Find the solution of the differential equation:

(ax + hy + g)dx + (hx + by + f )dy = 0

b) Use the method of undermined coefficients to find the general solution of the

differential equation:

d^3y/dx^3 + d^2y/dx^2 = 3e^x + 4x^2

c) Solve the differential equation:

dy/dx - (3/2x)y = 2x/y

d) Use the method of variation of parameters to solve the differential equation:

y''' + 3y' + 2y = 4e^x

e) Find the integral curve of the differential equations:

dx/( x^2 - y^2 - z^2 ) = dy/2xy = dz/2xz

f) Find a particular integral of differential equation:

(D^3 - D' ^3)z = x^3 × y^3