Use Euler method to determine the approximation of given problem

[chwala]

Homework Statement

see attached

Relevant Equations

Numerical methods

There is a mistake in my opinion on the text. In my working i have,

$y_1= 3 + 0.2 e^{\cos1} = 3+ 0.54357 = 3.54357$
$y_2 = 3.54357 + 0.2 e^{\cos 1.2} = 4.0871$
$y_3 = 4.0871 + 0.2 e^{\cos 1.4} = 4.6305$

I also noted that we do not have an exact solution for this problem.

 

[Mark44]

Homework Statement: see attached
Relevant Equations: Numerical methods

View attachment 343068

There is a mistake in my opinion on the text. In my working i have,

$y_1= 3 + 0.2 e^{\cos1} = 3+ 0.54357 = 3.54357$
$y_2 = 3.54357 + 0.2 e^{\cos 1.2} = 4.0871$
$y_3 = 4.0871 + 0.2 e^{\cos 1.4} = 4.6305$

It's given that $y_1 = 3$ when $x_1 = 1$
$y_2 = 3 + 0.2e^{\cos(1)} \approx 3.343305$ which agrees with the value shown in the image.

 

[chwala]

It's given that $y_1 = 3$ when $x_1 = 1$
$y_2 = 3 + 0.2e^{\cos(1)} \approx 3.343305$ which agrees with the value shown in the image.

aaaaaaaah hahaha i was using degrees instead of radians. Silly of me @Mark44 do we have an exact solution to this problem?