English
Hindi

Question

Download Solution PDF

The solution of  will be

  4.  
  5. None of these

Answer (Detailed Solution Below)

Option 4 :  

Detailed Solution

Download Solution PDF

Concept:

Some useful formulas are:

Calculation:

⇒

Substituting y = vx and  

⇒ 

⇒ 

Integrating both sides we get,

⇒ , c = constant of integration

Putting the value of v we get,

∴ 

Download Solution PDF
Exams Tests Super Practice

More Solution of Differential Equations Questions

Q1.The differential equation of y = ex(A cos x + B sin x) is
Q2.The general solution of the differential equation \(\sec ^{2} y \frac{d y}{d x}+2 x \tan y=x^{3}\) is
Q3.The differential equation \(\frac{d y}{d x}+P y=Q y^{n} \) where P and Q are functions of x alone, can be reduced to linear form by dividing the equation by yn and putting
Q4.General solution of differential equation \(\rm \frac{dy}{dx}+y \cot x = cosec \ x\) is:
Q5.General solution of differential equation \(\rm \frac{dy}{dx}=\frac{y}{x}\) is:
Q6.If the 9-digit number 83P93678Q is divisible by 72, then what is the value of \(\sqrt {P^2+Q^2+12}\) ?
Q7.If x + \(\frac{1}{2x}\) = 3, then evaluate 8x3 + \(\rm \frac{1}{x^3}\).
Q8.If x2 + y2 + z2 = xy + yz + zx and x = 1, then find the value of \(\rm \frac{10x^4+5y^4+7z^4}{13x^2y^2+6y^2z^2+3z^2x^2}\)
Q9.Find the solution of the differential equation \(\rm \frac{dy}{dx}=e^{x+y}+x^2e^y\)
Q10.The solution of the differential equation dy = (1 + y2)dx 

More Differential Equations Questions

Q1.If y = y(x) is the solution of the differential equation \(e^y\left(\frac{d y}{d x}-1\right)=e^x\) such that y(0) = 0, then y(1) is equal to
Q2.If a curve y = f(x) passes through the point (1, 2) and satisfies xdy/dx + y = bx4, then for what value of b, \(\int_1^2 f(x) d x=\frac{62}{5}\)
Q3.The general solution of the differential equation (x – y2) dx + y (5x + y2)dy = 0 is :
Q4.If the solution y = y(x) of the differential equation (x4 + 2x3 + 3x2 + 2x + 2)dy – (2x2 + 2x + 3)dx = 0 satisfies \(y(-1)=-\frac{\pi}{4}\), then y(0) is equal to:
Q5.If y = y(x) is the solution of the differential equation \(\rm \frac{dy}{dx}+2y=\sin (2x), y(0)=\frac{3}{4}\), then \(\rm y\left(\frac{\pi}{8}\right)\) is equal to 
Q6.The solution of \(x \frac{d y}{d x}+y=y^{2}\) is
Q7.The differential equation of y = ex(A cos x + B sin x) is
Q8.If \(y=e^{a \cos ^{-1} x}\), -1 < x < 1, then the value of \((1-x^{2}) \frac{d^{2} y}{d x^{2}}-x \frac{d y}{d x}\) is
Q9.The general solution of the differential equation \(\sec ^{2} y \frac{d y}{d x}+2 x \tan y=x^{3}\) is
Q10.The differential equation \(\frac{d y}{d x}+P y=Q y^{n} \) where P and Q are functions of x alone, can be reduced to linear form by dividing the equation by yn and putting

More Mathematics Questions

Q1.log10 10000 = _______?
Q2.Consider a system equation \(2x+y-z=0\), \(4x - py + 4z = 4\) and \(x-y+z=q\) where \(p, q \in I\) and \(p, q \in [1, 10]\), then identify the correct statement(s).   List-I List-II (I) Number of ordered pairs \((p, q)\) for which system of equation has unique solution is (P) 1 (II) Number of ordered pairs \((p, q)\) for which system of equation has no solution is (Q) 9 (III) Number of ordered pairs \((p, q)\) for which system of equation has infinite solution is (R) 91 (IV) Number of ordered pairs \((p, q)\) for which system of equation has atleast one solution is (S) 90
Q3.Match List I with List II:   List - I List - II (I) The number of solutions of the equation\((1 - \cos 2x)(\cos 2x + \cot^2 x) = 0\) where \(0 \le x \le 2\pi\) is (P) 4 (II) \(\tan 81^\circ - \tan 63^\circ - \tan 27^\circ + \tan 9^\circ\) equals (Q) 3 (III) The number of solutions of (x, y), which satisfy |y| = sin x and y = cos-1(cos x), where -2π ≤ x ≤ 2π is (R) 2 (IV) For the equation \(\cos^{-1}x + \cos^{-1}2x + \pi = 0\), the number of real solutions is (S) 1     (T) 0  
Q4.If Σn = 36, find n
Q5.If log 2 = 0.2614, log 3 = 0.3521, log 6 = ?
Q6.The growth model for a population is Nt = N0ert where Nt is the population at time t, N0 is the initial population and r is the per capita growth rate. How long does it take for the population numbers to double?
Q7.Suppose that the growth rate of the number of individuals (N) in a population in an environment with a carrying capacity K is modelled as \(\frac{d N}{d t}=r N \frac{K-N}{K}\) where r is the per capita growth rate and t is time; r and K are positive constants. At which of the following values of N will the population growth rate be the maximum?
Q8.The shadow of a vertical pole, formed due to a nearby lamp which is at a height of 12 m, measures 4 m. If the lamp is moved horizontally 2 m further away from the pole, the length of the shadow measures 8 m. What is the height (in m) of the pole?
Q9.A pack of cards contains 4 aces, 4 kings, 4 queens and 4 jacks. Out of these 16 number of cards, two cards are drawn at random. Find the probability that at least one of them is an ace :
Q10.If the equations 2x2 + kx - 5 = 0 and x2 - 3x - 4 = 0 have one root common, then find the value of k.
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 apk download dhani teen patti real cash teen patti rummy teen patti