I have this BVP $$u''+u' =f(x)-\lambda |u(x)| $$, ##x\in [0,1]## we BC ## u(0)=u(1)=0##.(adsbygoogle = window.adsbygoogle || []).push({});

Following an ''algorithm'' for calculating the green's function I got something like $$g(x,t)=\Theta(x-t)(1+e^{t-x}) + \frac{e^{t}-e}{e-1} +\frac{e-e^{t}}{e-1}e^{-x}$$. At some point there is this integral ##j(x)=- \int_{0}^{1}g(x,t)dt ## and since ## j(0)=j(1)=0 , j'' + j'=-1## which leads to ## j(x)= \frac{e}{e-1} -x -\frac{e}{e-1}e^{-x}##

Can someone show me how it goes from defining the integral to find this form of ##j(x)##. I mean for the conditions I see there is a straight connection with our initial form BC. For the second I understand that the differential operator acts on j(x) but why it gives -1 and how j(x) takes the final form?

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# A Green's Function ODE BVP

Have something to add?

Draft saved
Draft deleted

**Physics Forums | Science Articles, Homework Help, Discussion**