Solve x^2 p+ y^2 q =z^2.
Answers
Answered by
1
Answer:
9x2−9(p+q)x+(2p2+5pq+2q2)=0
Step-by-step explanation:
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Answered by
1
Answer:
0 is the ans
Step-by-step explanation:
The Lagrange auxiliary equation is
x
2
dx
=
y
2
by
=
z
2
DZ
x
2
dx
+
y
2
by
−2
z
2
DZ
=0
Choosing(
x
2
1
,
y
2
1
,−2
z
2
1
)as multipliers.
∫
x
2
dx
+∫
y
2
by
−2∫
z
2
DZ
=0
−
x
1
−
y
1
+2
z
1
=C
x
1
+
y
1
−2
z
1
=C
yz+xz−2xy=Cxyz
Letzte constant.
It implies
x
2
dx
−
y
2
by
=0.
∫
x
2
dx
−∫
y
2
by
=0
−
x
1
=−
y
1
+ϕ(z),
x
1
−
y
1
=−ϕ(z)
y−x=ϕ(z)xy
x
1
−
y
1
=−ϕ(z)
−
x
2
1
+
y
2
1
dx
by
=
DZ
d(ϕ(z))
⋅
dx
DZ
x
2
dx
−
y
2
by
=−
DZ
d(ϕ(z))
⋅DZ
x
2
dx
−
y
2
by
=0⋅DZ
DZ
d(ϕ(z))
=0
d(ϕ(z))=0⋅dz
∫d(ϕ(z))=∫0⋅dz
∴ϕ(z)=C
y−x=Cxy
ϕ(
x
1
−
y
1
,
x
1
+
y
1
−
z
2
)=0, is the solution to the PDE
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