Answer to Question #189794 in Differential Equations for Soumitra Barik

Question

X²u_xx +2xyu_xy+u_yy=u

Answer 1

(Note - nothing is asked in question , so I am giving basic idea to approach these types of problems)

Solution:-

$x^2u_{xx} +2xyu_{xy}+u_{yy}=u$

$On \ solving \ we \ got \\$

$A= x^2 \\ B = 2xy \\ C = 1$

Now use

$b^2-4ac =0$

To check it is which type of curve this is

$4x^2y^2 - 4x^2= 0 \\ 4x^2(y^2-1)=0$

$\implies$

$x=0 , y= +1,-1$

After deciding the curve

Also we can find the colonial form.

As several things .