Let y(x) be the solution of the following initial-value problem. dy dx (a) Use Euler's method and technology to compute y(1) with each of the following step sizes. + 3x²y = 18x2, y(0) = 7 (i) h = 1 y(1) = (ii) h = 0.1 y(1) = (iii) h = 0.01 y(1) = (iv) h = 0.001 y(1) = (b) Verify that y = 6 + e-x³ is the exact solution to the differential equation. We have y = 6 + e-x³ ⇒ y'=

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