Consider the following differential equation, with time domain t e (0,1): y" = 2ty +t²y', y(0) = 1, y'(0) = 0. Solve it with the following methods: • Euler's method with h = 1, • Backward Euler's...

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Extracted text: Consider the following differential equation, with time domain t e (0,1): y" = 2ty +t²y', y(0) = 1, y'(0) = 0. Solve it with the following methods: • Euler's method with h = 1, • Backward Euler's method with h = 1, • non self starting Heun's method, with y1 = 0, and step size h = 1.