1. The problem statement, all variables and given/known data I posted this already but decided to revive this thread since I re-worked the problem. Consider dy/dx=x+y, a function of both x and y subject to initial condition, y(x0)=y0. Use Taylor series to determine y(x0+[itex]\Delta[/itex]x) to 4th order accuracy. Initial condition: x0=0, y(x0)=1 step size: [itex]\Delta[/itex]x=0.1 Show 5 significant digits in the answer. Do the calculations for only one step. 2. Relevant equations [itex]\epsilon[/itex]=O([itex]\Delta[/itex]x5) 3. The attempt at a solution dy/dx=f(x,y) Taylor series: y(x0+[itex]\Delta[/itex]x)=y(x0)+[itex]\Delta[/itex]xf'(x0,y(x0))+ \Delta[/itex]x21/2!f''(x0,y(x0))+[itex]\Delta[/itex]x31/3!f'''(x0,y(x0))+[itex]\Delta[/itex]x41/4!f''''(x0,y(x0))+[itex]\epsilon[/itex]+[itex] Is this correct? My solution: The derivatives: f'(x,y)=dy/dx=y+x=1+0=1 f''(x,y)=d2y/dx2=dy/dx+1=1+1=2 f'''(x,y)=d3y/dx3=dy2/dx2=2 f''''(x,y)=d4y/dx4=d3y/dx3=2 y(0+.1)=1+(.1)(1)+1/2!(.1)2(2)+1/3!(.1)3(2)+1/4!(.1)4(2)+(.1)5 y(.1)=1+.1+.01+.001/3+.0001/12+.00001=1.11035 Did I solve this correctly? I want to be able to have something decent when I meet with the professor tomorrow.