I am more accustomed to write y= ux but your method is equivalent.mamma_mia66 said:Homework Statement
y2dx -x(2x+3y)dy =0 I have to recognize the equation and solve it
Homework Equations
The Attempt at a Solution
I did y2dx - (2x2+ 3yx) dy=0
which is a homogeneous now
after I substitude x=uy
dx=udy + ydu
I stuck here after the substitution
y2udy+y3du - 2x2dy + 3yxdy=0
please someone help if I am not in right direction from the begining.
A homogeneous equation is a type of differential equation in which all terms have the same degree. This means that all terms are raised to the same power, making the equation easier to solve.
To solve a homogeneous equation, you can use the substitution method. This involves substituting y = vx into the equation, where v is a new variable, and then solving for x in terms of v. Once you have a solution for x, you can substitute it back into the original equation and solve for y.
The degree of a homogeneous equation is the highest power to which any variable is raised. For example, the degree of y2dx -x(2x+3y)dy =0 is 2, since both y and x are raised to the power of 2.
Yes, a homogeneous equation can have non-constant coefficients. In fact, most homogeneous equations have non-constant coefficients, making it necessary to use the substitution method to solve them.
Solving a homogeneous equation allows us to find a general solution that can be used to solve a variety of problems in different fields of science and engineering. It is also a useful tool in understanding the behavior of systems that exhibit symmetry, as homogeneous equations often describe these types of systems.