Question

1 For solving the Laplace equation: na Pu= y + y = 0 in D. Fu = ir tuvu = n(0.4) = 0 (0 < y < b) . u(a,y) = f(u), (0 < y < b) . u(x,0)= u(x,b)=0, (0<x<a)
we apply the boundary conditions in the order ?
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Answer 1

Given equation is 5x+19y=64

We need to look for integers x and y that satisfy the above equation.

Let us find a solution for 5x+19y=1

We are doing this because when we will multiply that equation by 64 we will get as follows:

64×5x+64×19y=64×1

Which can be written as 5×(64x)+19×(64y)=64 thus giving two integer 64x and 64y as solution for our required equation.

So let us find a solution for 5x+19y=1.So with basic idea we observe x=4,y=−1 works.

So we have a solution for our given equation 5x+19y=64 as 64×4 and 64×−1.

With this solution we see that options A,B are incorrect.

Now let us look at Option D.

y should be multiplied with such a value which when added to RHS 64 leads to its last digit as 5 or 0 so that it can be divided further by 5 to find value of x.So neither −58 nor −57 will work.

Hence option D is incorrect.

And we have already found x=64×4 gives us integer solution hence correct option is C.

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