(Solved):   please help asap thank you unction is \( y(t)=\{10-1) e t-(10-2)(t+1) \) 1. Verify that ...

 

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unction is \( y(t)=\{10-1) e t-(10-2)(t+1) \) 1. Verify that \( y(t) \) is a solution to the differential equation \( y^{\prime}=(10-2) t+y \) with initial \( y(0)=2-1 \). 2. Using stepsize \( \mathrm{h}=1 \), apply Euler Method, Modified Euler Method and Runge-Kutta Method once to find an approximation on \( y(1) \). 3. Calculate the relative error of approximation on \( y(1) \) for all of three methods. (You will get zero credit from this part if your answer is absolute error.)