Find an explicit solution of IVP for the diffusion equation:
$u_{t}=u_{xx}, x \in\ {R}, t>0$
$u(0,x)=x, x\in R$
So, I used the normalization integral, differentiated it in t and then rearranging the terms of that newly obtained equation I got that it equals to 2t. And then substituted the integrals which yield the closed explicit expression for u(x,t)=......=x
Could someone confirm that it's a correct solution or if it's not, could you please post how you solved this problem so I can figure out where I made a mistake!
Thank you so much! Would highly appreciate your help!