Q. Obtain the partial differential equation by eleminating the arbitrary constant from the relation u=ax+(1-a)y+b

Question

This question is about formation of P.D.E.

Answer 1

Q. Obtain the partial differential equation by eliminating the arbitrary constant from the relation u=ax+(1-a)y+b

 

There are two arbitrary constants here, a and b.

 

Differentiating u wrt x,

ꝺu/ꝺx = a

Differentiating u wrt y,

ꝺu/ꝺy = (1-a)

ꝺu/ꝺy + a = 1

Substituting for a = ꝺu/ꝺx,

ꝺu/ꝺx + ꝺu/ꝺy = 1

 

Answer 2

Differentiate given equation w. r. to x and y partially

We get derivative of u wr to x is a

And w. r to y is (1-a)

From this we get del u over x+del u over y=1.