1. Earlier you learned how to solve some differential equations. Many times in a
ID: 2884479 • Letter: 1
Question
1. Earlier you learned how to solve some differential equations. Many times in application you can't, so you approximate the solution by uig a Taylor series! In this question we'll approximate a solution to y'(r) = r2 + y2, y(1) = 0 (a) Find y'(1) from the equation. (b) Differentiate both sides of the equation to obtain y"(x) (you don't need to sub in y'(x) after) (c) Use the previous two results to obtain y"(1). (d) Continue the process to find y"(1) and y). (e) Use the previous step to form the fourth order Taylor series that approximates y(r).Explanation / Answer
y ' = x2+y2
y'(x)=x2+y(x)2
a. y'(1)=1+y(1)2=1+0=1
b. y ' =x2+y2
Differentiating
y ''= 2x +2y y'
c. y''(1)=2(1)+2(0)(1) =2
d. y '' = 2x +2y y'
Differentiating
y ''' = 2 + 2 (y')2+ 2y y''
y '''(1)= 2+ 2+ 0 = 4
yiv= 2 + 4y'y''+2 (y')2+ 2y y''
yiv(1)=2+4(2)+2+0=12
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.