Question

[75 pts] A system is defined by the following matrix equation: 5 50 10||Jal+|-120 1500 90|| 0 10 251 ly3l L-270 90 400 JLy3 slel-1-000-120-170E」 2 x 105-105 +1-105 2x105 011Y2 with initial conditions: ỹ"(0) = [0.1, 0.2, 0.3] and y"(0) = [3,-2, 1]

Answer 1

The function f(x, y) = x^2 + y^2 is homogenous of degree s, Since f(zx, zy) = (zx)^2 + (zy)^2 = z^2 (x^2 + y^2) = z^2 f(x, y). Example 2, the function f(x, y) = squareroot x^8 - 3x^2 y^6 is homogeneous of degrees 4, since f(zx, zy) = squareroot (zx)^8 - 3(zx)^2 (zy)^6 = squareroot z^8(x^8 - 3x^2 y^6) = squareroot z^8 squareroot x^8 - 3x^2 y^6 = z^4 f(x, y) Example 3, the function f(x, y) = 2x + y is homogeneous of degree 1, since f(zx, zy) = 2(zx) + (zy) = z(2x + y) = z^' f(x, y) Example 4: the function f(x, y) = x^3 - y^2 is not homogenous, since f(zx. Zy) = (zx)^3 - (zy)^2 = z^3 x^3 - z^2 y^2.