The differential equation is to be solved for Obtain the solution to the initial value problem for (l) with y(0) =1 y(0) = -2 using the second-order Taylor series method by introducing the variable; (x) - dy/dx. Deduce the algorithm valid for with J l/h. x} - jh. y, = s(x,) etc Note. the algorithm is not valid for j = 0. Obtain yt from the initial data at r0 - 0 bf writing y(x) as a Taylor series about x = 0 of appropriate order and substituting it into (I) to deduce the coefficients. Use a step-size h = 0.1 to obtain the solutions from (2) and (3). Display your results in the following format
Show transcribed image textThe differential equation is to be solved for Obtain the solution to the initial value problem for (l) with y(0) =1 y(0) = -2 using the second-order Taylor series method by introducing the variable; (x) - dy/dx. Deduce the algorithm valid for with J l/h. x} - jh. y, = s(x,) etc Note. the algorithm is not valid for j = 0. Obtain yt from the initial data at r0 - 0 bf writing y(x) as a Taylor series about x = 0 of appropriate order and substituting it into (I) to deduce the coefficients. Use a step-size h = 0.1 to obtain the solutions from (2) and (3). Display your results in the following format