Hindi
English

Question

Download Solution PDF

α और β के मान क्या हैं जो  एक सटीक अवकल समीकरण बनाते हैं?

This question was previously asked in
UPSC IES Electrical 2022 Prelims Official Paper
Download PDF Attempt in App
View all UPSC IES Papers >
  1. α = -1, β = -2
  2. α = 1, β = -2
  3. α = -1, β = 2
  4. α = -2, β = -1

Answer (Detailed Solution Below)

Option 1 : α = -1, β = -2
Free Tests
View all Free tests >
Free
ST 1: UPSC ESE (IES) Civil - Building Materials
20 Qs. 40 Marks 24 Mins
Start Now

Detailed Solution

Download Solution PDF

अवधारणा:

एक सटीक अवकल समीकरण पर विचार करें:

M dx + N dy = 0

एक सटीक अवकल समीकरण की स्थिति:

गणना:

दिया गया है, 

 और 

α = -1, β = -2

Download Solution PDF
Latest UPSC IES Updates

Last updated on Jul 2, 2025

-> ESE Mains 2025 exam date has been released. As per the schedule, UPSC IES Mains exam 2025 will be conducted on August 10. 

-> UPSC ESE result 2025 has been released. Candidates can download the ESE prelims result PDF from here.

->  UPSC ESE admit card 2025 for the prelims exam has been released. 

-> The UPSC IES Prelims 2025 will be held on 8th June 2025.

-> The selection process includes a Prelims and a Mains Examination, followed by a Personality Test/Interview.

-> Candidates should attempt the UPSC IES mock tests to increase their efficiency. The UPSC IES previous year papers can be downloaded here.

Exams Tests Super Practice

More Exact Differential Equations Questions

Q1.α और β के मान क्या हैं जो \(dF(x, y)=\left(\frac{1}{x^2+2}+\frac{\alpha}{y}\right)dx\space + (xy^\beta+1)dy\) एक सटीक अवकल समीकरण बनाते हैं?
Q2.For the exact differential equation, \(\frac{du}{dx}=\frac{-xu^2}{2+x^2u}\) which one of the following is the solution?
Q3.अवकल समीकरण \(y^3\frac{dy}{dx}\;+\;x^3=0\), y(0) = 1 का हल y द्वारा दिया गया है। y(-1) का मान है:
Q4.General solution of the equation (x3 + 3xy2)dx + (3x2y + y3)dy = 0 is (c is a constant)
Q5.The solution of the differential equation \(\frac{{dy}}{{dx}} - \frac{{ - x}}{y}\) at x = 1 and \(y = \sqrt 3\) is 
Q6.अवकल समीकरण \(\dfrac{dy}{dx}(x \log x) + y = 2\log x\) का समाकलन कारक क्या है?
Q7.अवकल समीकरण 2y dx – (3y – 2x) dy = 0 _________________ होता है।
Q8.The differential equation satisfying y = \(A{e^{3x}} + B{e^{2x}}\) is 
Q9.The general solution of the differential equation 9yy’ + 4x = 0 is, \(\left( {{\rm{y'}} = \frac{{{\rm{dy}}}}{{{\rm{dx}}}},{\rm{\;C}} = {\rm{constant}}} \right)\)

More Differential Equations Questions

Q1.The partial differential equation obtained by eliminating φ from : φ(x + y + z, x2 + y2 − z2) = 0 is : 
Q2.अवकल समीकरण \(\frac{d y}{d x}=e^{x-y}+x^{2} e^{-y} \) का व्यापक हल क्या है?
Q3.The solution of the differential equation \(\rm \frac{d^3y}{dx^3}-5.5\frac{d^2y}{dx^2}+9.5\frac{dy}{dx}-5y=0\) is expressed as 𝑦 = 𝐶1𝑒2.5𝑥 + 𝐶2𝑒𝛼𝑥 + 𝐶3𝑒𝛽𝑥 , where 𝐶1, 𝐶2, 𝐶3, 𝛼, and 𝛽 are constants, with α and β being distinct and not equal to 2.5. Which of the following options is correct for the values of 𝛼 and 𝛽?
Q4.x2 + y2 = 2ax द्वारा दिए गए वक्र-कुल का अवकल समीकरण ________ है।
Q5.Consider the differential equation   \(\rm \frac{dy}{dx}+y ln(y)=0\) If 𝑦(0) = 𝑒, then 𝑦(1) is ________ 
Q6.A differential equation is given as x (t + 2) + 3x (t + 1) + 2x (t) =0; x(0) = 0, x(1) = 1. The solution of this equation will be: 
Q7.यदि \(\lambda=\frac{[1+(dy/dx)^2]^3}{(d^2y/dx^2)^{2/3}}\), तो उपर्युक्त अवकल समीकरण की घात तथा कोटि क्रमशः हैं?
Q8.फलन z = tan-1 \(\frac{y}{x}\) के लिए निम्न कथनों पर विचार कीजिए: \({S_1} \equiv x\frac{{\partial z}}{{\partial x}} + y\frac{{\partial z}}{{\partial y}} = 0\) \({S_2} \equiv {x^2}\frac{{{\partial ^2}z}}{{\partial {x^2}}} + 2xy\frac{{{\partial ^2}z}}{{\partial x\partial y}} + {y^2}\frac{{{\partial ^2}z}}{{\partial {y^2}}} = 0\) \({S_3} \equiv \frac{{{\partial ^2}z}}{{\partial {x^2}}} + \frac{{{\partial ^2}z}}{{\partial {y^2}}} = 0\) कौन सा/से कथन सत्य है/हैं?
Q9.यदि z = f(x + ay) + ϕ (x - ay), तब-
Q10.अंतर समीकरण y n +2 - 2y n+1 + y n = n 2 2 n का विशेष समाकल है
Suggested Test Series
View All >
UPSC ESE (IES) Civil Mock Test Series
116 Total Tests with 1 Free Tests
Start Free Test
UPSC ESE (IES) Prelims Paper 1 Mock Test Series
54 Total Tests with   1 Free Tests
Start Free Test

More Engineering Mathematics Questions

Q1.यदि L = {1, 2, 3, 4, 6, 9, 36} जालक है, तो नीचे दिए गए हैस आरेख में 9 के पूरकों की संख्या ज्ञात कीजिए।
Q2.अनिर्देशित आलेख के लिए निम्नलिखित में से कौन सा/से कथन सत्य है?
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 bodhi teen patti master king teen patti app teen patti winner teen patti live