(a) find the solution u(x, y)of laplace’s equation in the rectangle 0 (b) find the solution if g(x)=x,0≤x≤a/2,a−x, a/2≤x≤a.
(c) fora=3 and b=1, plot u versus x for several values of y and also plot u versus y for several values of x.
(d) plot u versus both x and y in three dimensions. also draw a contour plot showing several level curves of u(x, y)in the xy-plane.

Workings and solution to this question can be viewed in the screenshots below:

37/3

step-by-step explanation:

step 1: simplify both sides of the equation.

7x+8(x+

1

4

)=3(6x−9)−8

7x+(8)(x)+(8)(

1

4

)=(3)(6x)+(3)(−9)+−8(distribute)

7x+8x+2=18x+−27+−8

(7x+8x)+(2)=(18x)+(−27+−8)(combine like terms)

15x+2=18x+−35

15x+2=18x−35

tep 2: subtract 18x from both sides.

15x+2−18x=18x−35−18x

−3x+2=−35

step 3: subtract 2 from both sides.

−3x+2−2=−35−2

−3x=−37

step 4: divide both sides by -3.

−3x

−3

=

−37

−3

x=

37

3