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.

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- May 7th 2010, 12:55 AMbogazichiligeneral soltn by using mthd of characteristic
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. - May 7th 2010, 07:00 AMJester
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.