u_xx + 10u_xy + 9u_yy = y
how can we find this equation's general solution by using the method of characteristics? ı m new in this field.
gives the type. Here so it's hyperbolic which means we can transform it to standard form, i.e. . After a change of variables and choosing our target form, we find that and must satisfy
or (choose one for and the other for ).
so satisfies and satisfies . Each are easily solved giving
from which we choose simple
Under this change of variables we obtain
This we can integrate twice.