Let's find yβ² and yβ²β² :
y=Ax+Bx2
yβ²=A+2Bx (1)
yβ²β²=2B (2)
From (2) we have:
B=2yβ²β²β
Putting B into (1) we obtain:
yβ²=A+22yβ²β²βx=A+yβ²β²x
A=yβ²βyβ²β²x
Substituting A and B into the origin equation we get:
y=(yβ²βyβ²β²x)x+2yβ²β²βx2
2x2βyβ²β²βxyβ²+y=0
Answer: 2x2βyβ²β²βxyβ²+y=0 .
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