Use Euler method to determine the approximation of given problem

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chwala
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Homework Statement
see attached
Relevant Equations
Numerical methods
Slide titled Euler's Formula giving y(n+1) = yn + h f(xn), with dy/dx = f(x) and h the step size; worked example with dy/dx = e^(cos x), y = 3 at x = 1, step 0.2, reaching y = 3.631 at x = 1.4.


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.
 
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Discussion

chwala said:
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.
 
Mark44 said:
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 :wink: @Mark44 do we have an exact solution to this problem?