View Single Post
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
Flapping baby birds give clues to origin of flight
Prions can trigger 'stuck' wine fermentations, researchers find
Socially-assistive robots help kids with autism learn by providing personalized prompts