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(Solved): Use the Modified Euler method to approximate the solutions to each of the following initial-value p ...
Use the Modified Euler method to approximate the solutions to each of the following initial-value problems, and compare the results to the actual values. a. \( y_{1}^{\prime}=t e^{3 t}-2 y, \quad 0 \leq t \leq 1, \quad y(0)=0 \), with \( h=0.5 \); actual solution \( y(t)=\frac{1}{5} t e^{3 t}-\frac{1}{25} e^{3 t}+ \) \( \frac{1}{25} e^{-2 t} \).
Expert Answer
Solution: Given y?=te3t?2y,y(0)=0,h=0.5, 0?t?1 we have replaced t with x Here, x0=0,y0=0,h=0.5,xn=1 y?=xe3x?2y ?f(x,y)=xe3x?2y