10. [4 marks] Consider the initial value problem y" + xy - 20y = 0, y(0) = 1, y'(0) = 2. (a) By making appropriate subst

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10 4 Marks Consider The Initial Value Problem Y Xy 20y 0 Y 0 1 Y 0 2 A By Making Appropriate Subst 1 (42.17 KiB) Viewed 90 times

10. [4 marks] Consider the initial value problem y" + xy - 20y = 0, y(0) = 1, y'(0) = 2. (a) By making appropriate substitutions, show that this second-order problem can be rewritten as the following system of two first-order problems where z = 0 20 z'(x) = 1) 2 (1) | z(x), _z(0) = (2). = (b) Use two steps of Euler's method on the above system, with a step-size h z(1). Hence give an estimate for y(1). 0.5, to estimate