1. The problem statement, all variables and given/known data δu/δt+2tδu/δx=1 for t>0,x>0 with u= 0 on x= 0 for t>0, u=1 at t=0 for x≥0 2. Relevant equations 3. The attempt at a solution ((dx)/(dt))=2t x=t²+c x-t²=c the general solution is: u=t+F(x-t²) Now i am confused about the terminology for the domain, ie it says it is defined for t>0, x>0 I am confused about u= 0 on x= 0 for t>0 0=t+F(-t²) thus it follows that u(x,t)=t-√(t²+x) "at" x=o But what does it mean when is states this is only for t>0. For all t>0 when x is zero u will be zero anyway. The answer shows that the funcrtion u is equal to what i have solved for t²>x, and i can see that in this case the square root is defined(ie not √-) Then from the second condition the solution shows that u=1+t for t²≤x I would basically like to understand all this properly as i always get a bit confused with inequalities. How did they apply the second condition and inequality to get the second function and what was the reasoning?