1. Solve the initial value problem, dy = (* + xy )e, y (0) =1 With...

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1. Solve the initial value problem, dy = (* + xy )e, y (0) =1 With h = 0.1 %3D dx Use (i) Modified Euler's method to find y (0.1) (ii) Euler's method to find y (0.2). 2. Solve the initial value problem, dy I+x*) y, y(0) =1 With h = 0.1 dx %3D Use (i) the Improved Euler method to find y (0.1); (11) fourth order Runge Kutta method to find y (0.2). 3. Solve the initial value problem, dy = y - x, y(0.2) = 1.12 With h = 0.2 dx Use (i) the third order Runge Kutta method to find y (0.4); (1I) Euler method to find y (0.6). 1. Solve the initial value problem, dy = (* + xy )e, y (0) =1 With h = 0.1 %3D dx Use (i) Modified Euler's method to find y (0.1) (ii) Euler's method to find y (0.2). 2. Solve the initial value problem, dy I+x*) y, y(0) =1 With h = 0.1 dx %3D Use (i) the Improved Euler method to find y (0.1); (11) fourth order Runge Kutta method to find y (0.2). 3. Solve the initial value problem, dy = y - x, y(0.2) = 1.12 With h = 0.2 dx Use (i) the third order Runge Kutta method to find y (0.4); (1I) Euler method to find y (0.6).

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