Question #189794

X2uxx +2xyuxy+uyy=u


1
Expert's answer
2021-05-07T14:22:25-0400

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


Solution:-

x2uxx+2xyuxy+uyy=ux^2u_{xx} +2xyu_{xy}+u_{yy}=u


On solving we gotOn \ solving \ we \ got \\


A=x2B=2xyC=1A= x^2 \\ B = 2xy \\ C = 1


Now use

b24ac=0b^2-4ac =0

To check it is which type of curve this is


4x2y24x2=04x2(y21)=04x^2y^2 - 4x^2= 0 \\ 4x^2(y^2-1)=0


    \implies

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



After deciding the curve

Also we can find the colonial form.

As several things .


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