Given the following first-order ODE: dy dt =y+t³ , where t is evaluated from t = 0 to t= 1.5 with y(0) = 1 a. Solve the ODE using Euler's method (without an improvement) with step-size = 0.5 b. Solve the ODE using Euler's method (with an improvement) through Heun's method with step-size = 0.5 c. Give short analysis on methods used in a and b.

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