1
$\begingroup$

$$u u_x + (y + 1) u_y = u , x ∈ R, y > 0$$ $$u(x,0)=-3x, x ∈ R $$

I found the solution of the above initial value problem to be $$u(x,y)= \frac{-3x(y+1)}{(-3y+1)} $$

If someone could confirm this it would be fantastic. How do I sketch the characteristic base curves and define the region where the solution can be determined?

$\endgroup$
1
$\begingroup$

The characteristic base curves are the straight lines $x = s(1−3y)$. Where these lines intersect at the point$ (0, 1/3) $ .

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.