Question

Download Solution PDF

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 

This question was previously asked in
CSIR-UGC (NET) Mathematical Science: Held on (2024 June)
Attempt in App
View all CSIR NET Papers >
  1. 0
  2. -1
  3. 2
  4. 1

Answer (Detailed Solution Below)

Option 4 : 1
Free Tests
View all Free tests >
Free
Seating Arrangement
10 Qs. 20 Marks 15 Mins
Start Now

Detailed Solution

Download Solution PDF

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.

Download Solution PDF
Latest CSIR NET Updates

Last updated on Jun 5, 2025

-> The NTA has released the CSIR NET 2025 Notification for the June session.

-> The CSIR NET Application Form 2025 can be submitted online by 23rd June 2025

-> The CSIR UGC NET is conducted in five subjects -Chemical Sciences, Earth Sciences, Life Sciences, Mathematical Sciences, and Physical Sciences. 

-> Postgraduates in the relevant streams can apply for this exam.

-> Candidates must download and practice questions from the CSIR NET Previous year papers. Attempting the CSIR NET mock tests are also very helpful in preparation.

‹‹ Previous Ques
Next Ques ››
Exams Tests Super Practice

More Solutions of Differential Equations Questions

Q1.If the value of the approximate solution of the initial value problem   \(\rm \left\{\begin{matrix}y'(x)=x(y(x)+1), &x\in R\\\ y(0)=β \end{matrix}\right.\) at x = 0.2 using the forward Euler method with step size 0.1 is 1.02, then the value of β is 
Q2.If \(\frac{dy}{dx}\) = x - y2 and y(0) = 1, then y(0.1) correct upto two decimal places (approx.) is:
Q3.Runge-Kutta fourth order method is used to solve the differential equation \( \frac{dy}{dx} =( y~-~x)\). If the initial value y(0) = 2 and step-size is 0.1, then the value of y(0.1) is ______ (up to three decimal places)
Q4.A gradually varied flow profile can be governed by equation \(\dfrac{dy}{dx} = f(x,y)\) where x is distance and y is the depth of water above the bed level. Which of the following methods can be used for solution?
Q5.f(z) = (z − 1)−1 − 1 + (z − 1) − (z − 1)2 + ⋯ is the series expansion of
Q6.Solution of the differential equation (1 + 3x)dy - (1 - 3y)dx = 0, y(1) = 0 is
Q7.Using the method of variation of parameter solve y'' + y = sec x
Q8.If, \(\frac{{dy}}{{dx}} = x + y,y\left( 0 \right) = 1\) using Runge’s method the value of y at x = 0.2, when h = 0.2 is
Q9.Which of the following methods agrees with Taylor’s series solution up to term in h4?
Q10.The value of \({{\rm{\Delta }}^{10}}\left[ {\left( {1 - ax} \right)\left( {1 - b{x^2}} \right)\left( {1 - c{x^3}} \right)\left( {1 - d{x^4}} \right)} \right]\) is

More Numerical Methods Questions

Q1.The real root of the equation x3 − x − 5 = 0 lying between 1 and 2 after first iteration by Newton-Raphson method is ________, if initial approximation is taken as x0 = 2 ∈ [1, 2] : 
Q2.The rate of convergence of Newton Raphson method is :
Q3.If the value of the approximate solution of the initial value problem   \(\rm \left\{\begin{matrix}y'(x)=x(y(x)+1), &x\in R\\\ y(0)=β \end{matrix}\right.\) at x = 0.2 using the forward Euler method with step size 0.1 is 1.02, then the value of β is 
Q4.The iterative formula to find the root of the equation f(x) = x3 - 5x + 7 = 0 by the Newton Raphson method is ______.
Q5.In the Gauss elimination method for solving a system of linear algebraic equations, triangularization leads to-
Q6.If \(\frac{dy}{dx}\) = x - y2 and y(0) = 1, then y(0.1) correct upto two decimal places (approx.) is:
Q7.In which of the following categories can we put Bisection method?
Q8.Which order of Polynomials can best be integrated using Trapezoidal Rules?
Q9.Consider the differential equation \(\rm \frac{dy}{dx}=4(x+2)-y \) For the initial condition y = 3 at x = 1, the value of 𝑦 at x = 1.4 obtained using Euler’s method with a step-size of 0.2 is _________. (round off to one decimal place)
Q10.Consider the following recursive iteration scheme for different values of variable P with the initial guess x1 = 1. \(x_{n+1}=\frac{1}{2}\left(x_n+\frac{P}{x_n}\right)\), n = 1, 2, 3, 4, 5 For P = 2, x5 is obtained to be 1.414, rounded-off to three decimal places. For P = 3, x5 is obtained to be 1.732, rounded-off to three decimal places. If P = 10, the numerical value of x5 is ________. (round off to three decimal places)

More Engineering Mathematics Questions

Q1.If L = {1, 2, 3, 4, 6, 9, 36} is the lattice find the number of complements 9 is having in the below given Hasse diagram?
Q2.Which of the following statements is/are TRUE for undirected graphs?
Q3.\(\iint \frac{x y}{\sqrt{1-y^{2}}} d x d y\) Over the positive quadrant of the circle x2 + y2 = 1 is __________.
Q4.The real root of the equation x3 − x − 5 = 0 lying between 1 and 2 after first iteration by Newton-Raphson method is ________, if initial approximation is taken as x0 = 2 ∈ [1, 2] : 
Q5.Let X be uniform random variable on [0, 4] and Y be uniform random variable on [0, 1]. If X and Y are independent, then P(max {X, Y} > 3) is equal to : 
Q6.If R and D are the radius and diameter of the graph K4,7, then the ordered pair (R, D) is equal to : 
Q7.The largest number of faces in a simple connected maximal planar graph with 100 vertices is :
Q8.If for the matrix A, A3 = I then A−1 = __________. 
Q9.Energy of power signal is : 
Q10.With usual notations, the properties of maxima and minima under various conditions are __________. I II (P) Maxima (i) r t− s2 = 0 (Q) Minima (ii) rt − s2 < 0 (R) Saddle Point (iii) rt − s2 > 0, r > 0 (S)  Case of failure (iv) rt − s2 > 0, r < 0
Testbook Edu Solutions Pvt. Ltd.
1st & 2nd Floor, Zion Building,
Plot No. 273, Sector 10, Kharghar,
Navi Mumbai - 410210
support@testbook.com
Toll Free:1800 833 0800
Office Hours: 10 AM to 7 PM (all 7 days)
Company
About usCareers We are hiringTeach Online on TestbookPartnersMediaSitemap
Products
Test SeriesTestbook PassOnline CoursesOnline VideosPracticeBlogRefer & EarnBooks
Copyright © 2014-2022 Testbook Edu Solutions Pvt. Ltd.: All rights reserved
User PolicyTermsPrivacy
Hot Links： teen patti 50 bonus teen patti wink teen patti vungo