Obtain the Partial differential equation by eliminating the arbitary constants a
and b from z = (x2 + a) (y2 + b)
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(2+)(2+)
{\color{#c92786}{(x^{2}+a)(y^{2}+b)}}(x2+a)(y2+b)
(2+)⋅2+(2+)
{\color{#c92786}{(y^{2}+b) \cdot x^{2}+a(y^{2}+b)}}(y2+b)⋅x2+a(y2+b)
2
Distribute
(2+)⋅2+(2+)
{\color{#c92786}{(y^{2}+b) \cdot x^{2}}}+a(y^{2}+b)(y2+b)⋅x2+a(y2+b)
22+2+(2+)
{\color{#c92786}{x^{2}y^{2}+bx^{2}}}+a(y^{2}+b)x2y2+bx2+a(y2+b)
3
Distribute
22+2+(2+)
x^{2}y^{2}+bx^{2}+{\color{#c92786}{a(y^{2}+b)}}x2y2+bx2+a(y2+b)
22+2+2+
x^{2}y^{2}+bx^{2}+{\color{#c92786}{ay^{2}+ab}}x2y2+bx2+ay2+ab
4
Rearrange terms
22+2+2+
{\color{#c92786}{x^{2}y^{2}+bx^{2}+ay^{2}+ab}}x2y2+bx2+ay2+ab
22+2+2+
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