Introduction : Euler Method for system of differential equations Question : Solution: \[\left(\begin{array}{c}y_1′ \\y_2′ \end{array}\right)=\left(\begin{array}{cc}-t^2 & t \\2-t & 0 \end{array}\right)\left(\begin{array}{c}y_1 \\y_2 \end{array}\right)+\left(\begin{array}{c}1\\t \end{array}\right)\] f(t,y_1,y_2 )=-t^2 y_1+ty_2+1 g(t,y_1,y_2 )=(2-t) y_1+0y_2+t t_0=1 y_1,0=2,y_2,0=0 Euler method t_0=1 y_1,0=2,y_2,0=0 h=0.01 y_(1,n+1)=y_(1,n)+hf(t_n,y_(1,n),y_(2,n)) y_(2,n+1)=y_(2,n)+hf(t,y_(1,n),y_(2,n)) Step…
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