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| PAGE: 432 | SET: Exercises | PROBLEM: 53 |
The differential equation is 
.
Initial function is 
.
Perform Euler
s method for 
.
Step size is 
.
Eulers Method :
Using 
, 
, and 
.
Substitute 
, ,
and 
Substitute 
,
,
and
Simillarly,
.
(b)
The differential equation is .
Rewrite the function.
Apply integral on each side
Integral formula: 
.
Power rule of integration: 
.
Apply exponential on each side
Substitute 
in the integral function.
Substitute 
in the integral function.
Substitute in the above equation.
(c)
Find error.
The value of particular solution at using Eulers method is 
.
The value of the particular solution at is 
.
Error is 
.
(a) The value of particular solution at using Eulers method is 
.
(b) The value of the particular solution at is .
(c) Error is 
.
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