Given the differential equation y' = 4 cos(5y) and y(0) = 27 1. Use implicit derivatives to find "y" ", and "y"" 2. Use the initial value "y(0) = 2" to find the value of "y'(0)", "y"(0)", and "y"(0)". then plug them into the Taylor Series Polynomial formula. 2л x° + O! 20 x! + 1! - 100 x3 + (A) y(x) = x? + %3D ... 2! 3! By(x) 2л 87 x' + -40 - 200n x2 + r3 + ... 0! 1! 2! 3! - 360 x* + 3! -48 O y(x) - x0 + - ... O! 1! 2! - 100 y(x) 0! x' + 1! x2 + 2! ... 3! Ey(x) -20 x2 + r3 +... - O! 1! 2! 3! - 1600 y(x) 2л x° + O! 4 x! + 1! F x2 + 2! ... 3! + + +
Given the differential equation y' = 4 cos(5y) and y(0) = 27 1. Use implicit derivatives to find "y" ", and "y"" 2. Use the initial value "y(0) = 2" to find the value of "y'(0)", "y"(0)", and "y"(0)". then plug them into the Taylor Series Polynomial formula. 2л x° + O! 20 x! + 1! - 100 x3 + (A) y(x) = x? + %3D ... 2! 3! By(x) 2л 87 x' + -40 - 200n x2 + r3 + ... 0! 1! 2! 3! - 360 x* + 3! -48 O y(x) - x0 + - ... O! 1! 2! - 100 y(x) 0! x' + 1! x2 + 2! ... 3! Ey(x) -20 x2 + r3 +... - O! 1! 2! 3! - 1600 y(x) 2л x° + O! 4 x! + 1! F x2 + 2! ... 3! + + +
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
12
Transcribed Image Text:Given the differential equation
y' = 4 cos ( 5y) and y(0) = 2n
1. Use implicit derivatives to find "y"", and "y""
2. Use the initial value "y(0) = 2" to find the value of "y'(0)", "y"(0)". and "y"(0)". then plug them into the Taylor Series Polynomial
formula.
A y(x)
2л
x° +
O!
20
x' +
1!
- 100
x3 +
x2
...
2!
3!
By(x)
2л
-40
x2
- 200n
x! +
r3 + ...
+
0!
1!
2!
3!
- 48
- 360
© y(x)
-
x° +
x' +
+
-
...
O!
1!
2!
3!
- 100
r3
D.
y(x)
0!
x' +
1!
x2 +
2!
-..
3!
E y(x)
-20
+
x2
+
3!
r3 +...
-
O!
1!
2!
- 1600
y(x)
2л
x° +
O!
4
x! +
1!
F
x2 +
2!
...
3!
+
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