Step size 05 to compute the approximate yvalues y1 y2 y3 and

Solution

Step size h= 0.5 to compute the approximate y-values y1, y2, y3, and y4 of the solution of the initial-value problem y\'= 2-5x-2y y(1)=-4. y(xo) = yo x0=1 y0=-4 y\'= f(x,y) =2-5x-2y ==>yo=-4 y1= y(x1)=y(xo+h) = y(xo) + h*f(xo,yo) ==>y1= y(1.5) = -4 + 0.5*(2-5*(1)-2(-4)) = -1.5 ==>y2= y(2) = -1.5 + 0.5*(2-5*(1.5)-2(-1.5)) = -2.75 ==>y3= y(2.5) = -2.75 + 0.5*(2-5*(2)-2(-2.75)) = -4 ==>y4= y(3) = -4 + 0.5*(2-5*(2.5)-2(-4)) = -5.25