Solve the DE. (Homogeneous DE) 1. (3x2 + 9xy + 5y2)dx - (6x2 + 4xy)dy = 0
Homogeneous DE
M(x,y)dx + N(x,y)dy = 0
is Homogeneous if both M and N are homogeneous functions of the same order.
A function f(x,y) is called homogeneous of degree n if
f(ʎx, ʎy) = ʎnf(x,y)
Solution Steps:
Objective: To reduce into a Variable Separable Form
a. Replace y by ux or x by vy
if y = ux, dy = udx + xdu . Use y=ux if N is simpler in form.
if x = vy, dx = vdy + ydv . Use x=y if M is simpler in form
b. Simplify the resulting equation
c. Separate the variables
d. Integrate both sides of the equation to get the General Solution
e. Substitute u = y/x or v = x/y to have the GS in terms of x and y
have C which is arbitrary constant
Solve the DE. (Homogeneous DE)
1. (3x2 + 9xy + 5y2)dx - (6x2 + 4xy)dy = 0
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 3 images
