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.
First we will determine the type. Then general form of linear PDEs is
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.