View Single Post
QuarkCharmer
#1
Jan22-12, 08:38 PM
QuarkCharmer's Avatar
P: 1,035
For example:
[tex]\frac{dy}{dx} + y = e^{3x}[/tex]



I understand that these differential equations are most easily solved by multiplying in a factor of integration, and then comparing the equation to the product rule to solve et al..

For example:

[tex]t\frac{dy}{dx} + 2t^{2}y = t^{2}[/tex]
[tex]\frac{dy}{dx} + 2ty = t[/tex]

Multiplying in an integration factor u(x), which in this case:
[tex]u(x) = e^{\int{2t}dt} = e^{t^{2}}[/tex]

[tex]e^{t^{2}}\frac{dy}{dx} + 2te^{t^{2}}y = te^{t^{2}}[/tex]

Now I can compress the left side down using the product rule and all that.

I don't understand how they are getting u(x) or why it's equal to e^{\int{2t}dt} ?
Phys.Org News Partner Science news on Phys.org
Experts defend operational earthquake forecasting, counter critiques
EU urged to convert TV frequencies to mobile broadband
Sierra Nevada freshwater runoff could drop 26 percent by 2100