Problem #3 (16 points) Solve the following differential equation, dy - 2t+6y² = 0 dt using the Modified Euler Method (also called the Trapezoidal Method) with At₁ = 0.1s and initial value, y(0) = 1, and carry out the calculation again with a time step of At₂ = 0.05s and the same inital value. 18. The re-arrangement of the problem so that it can be solved by standard methods such as the Modified Euler Method is dy (a) = -2t+6y2 dt dy (b) = - 6y²+2t (c) dt dy dt (d) dy (e) - - 5y² = - 4t = - -6y²+4t none of the above 19. report the solution at t = 0.1s using the At₁ = 0.1s time step to five decimal place (rounding up). (a) y(0.1)=0.662 (b) y(0.1)=0.652 (c) y(0.1)=0.637 (d) y(0.1)=0.649 (e) none of the above anibouot moniq laminab cws of se 20. report the solution at t = 0.1s using the At₂ = 0.05s time step to two decimal place (rounding up). (a) y(0.1)=0.662 (b) y(0.1)=0.652 (c) y(0.1) = 0.637 (d) y(0.1)=0.649 (e) none of the above 21. report an error estimate for the solution using the 0.1s time step to one decimal place (rounding up). (a) error = 0.002 (b) error = 0.994 (c) error = 0.017 (d) error = 0.043 (e) none of the above