1. Consider the following first-order ODE: dị y t dx from x = 0 to x = 1.5 with y(0) = 1 (a) Solve by hand with Euler's explicit method using h = 0.5. (b) Solve by hand with the modified Euler method using h = 0.5- (c) Solve by hand with the classical fourth-order Runge-Kutta method using h = 0.5. The analytical solution of the ODE is: y=x²-e² +2. In each part, calculate the error between the true solution and the numerical solution at the points where the numerical solution is determined.

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