2) Laplace equation ux (0, y) = Uxx + Uyy 0, u(7, y) = 0 u(x, 0) 0 < x <7, 0 < y < 4, 0 < y < 4, 0 0 < x < 7 u(x, 4) = COS 2 (1) 0 < x < 7.
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using the method of separation of variables, solve the problem attached
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- Transform the equation: 2x2y'' + xy' + 3y = 0 to the form of: a(d2y/dz2) + b(dy/dz) + cy = 0 (a, b, c) = a) (2,1,-3) b) (2,-1,3) c) (-2,1,4) d) (2,-1,4) e) (2,0,0)Find y in terms of x. dy = x 4(x 5 - 3) 2, curve passes through (1, 5) dx 17 A y = - (x5 -3) 3 + 15 1 B) y = x 15-3 + 15 27 с) у3 - (x 5 - 3) 1+ 83 D y = (x 5 - 3) 3 + 15 15linearise R = AT + BT2
- Use the graph to estimate the slope of the tangent line to y = x" at the given point. Verify your answer analytically. (a) y = x1/2, (9, 3) 10 8 y 4- (9, 3) 2- 4 6 8 10 y' = 3Find the linearization L(x, y) of the function f(x, y) = (x^3)(y^6) at the point (-2, -2).the linearization of (fi,f2) = (x²y+ 3xy², 3x³ + 2xy) at (1,0) to approximate the value at (0.9,-0.1).