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If the value of the approximate solution of the initial value problem  

at x = 0.2 using the forward Euler method with step size 0.1 is 1.02, then the value of β is 

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  3. 2
  4. 1

Answer (Detailed Solution Below)

Option 4 : 1
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Detailed Solution

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Concept: 

Euler's Method: 

 

Explanation:

Given,

The differential equation 

Initial condition   and Step size  

The value of the approximate solution at  using the forward Euler method is 1.02.

We are asked to find the value of  .


Euler's method is a numerical technique to approximate the solution of initial value problems.

The formula for Euler's method is 

 

The derivative given in this problem is ) , so .


We are given that   and need to compute the value of  at .

Let's start by applying Euler's method iteratively, starting at  .

Initial Condition:

At  , we have 


⇒ 

So, after the first step,  .


⇒ 

⇒ 

We are given that   at .


From the equation , we know 

⇒ 
 

⇒ 

⇒ 

The value of  is 1.

Hence option 4) is correct.

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