Diff eq, need a simple step explained

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In summary, the given step involves expanding and simplifying expressions, leading to the substitution of y=ux in a few steps back. It is a part of solving a homogeneous DE using the method of substitutions.
  • #1
frozenguy
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So its not a problem, but a step in an example that I need explained. The section is solutions by substitutions and its an example of solving a homogeneous DE.

Step goes from:
[tex]\left(x^{2}+u^{2}x^{2}\right)dx+\left(x^{2} - ux^{2}\right)\left[udx + xdu\right]=0[/tex]

to:
[tex]x^{2}\left(1 + u\right)dx + x^{3}\left(1-u\right)du=0[/tex]

It had previously set y=ux, a few steps back.
 
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  • #2
frozenguy said:
So its not a problem, but a step in an example that I need explained. The section is solutions by substitutions and its an example of solving a homogeneous DE.

Step goes from:
[tex]\left(x^{2}+u^{2}x^{2}\right)dx+\left(x^{2} - ux^{2}\right)\left[udx + xdu\right]=0[/tex]
Just expand the expressions above, and simplify.
[tex](x^2 + u^2x^2 + x^2u - u^2x^2)dx + (x^3 - ux^3)du = 0[/tex]
frozenguy said:
to:
[tex]x^{2}\left(1 + u\right)dx + x^{3}\left(1-u\right)du=0[/tex]

It had previously set y=ux, a few steps back.
 
  • #3
Thank you... I don't know why I didn't see this before.. Ok I feel stupid. :/
 

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A differential equation is a mathematical equation that describes the relationship between a function and its derivatives. It is used to model a wide range of natural phenomena in fields such as physics, biology, and economics.

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