If xdydx=y(log y−log x+1), then the solution of the equation is

Sail E0 Webinar

Question

If

x \frac{d y}{d x} = y (l o g y - l o g x + 1)

, then the solution of the equation is

Options:

A . y log(xy)=cx

B . x log(yx)=cy

C . log(yx)=cx

D . log(xy)=cx

Answer: Option C
:
C

\frac{d y}{d x} = \frac{y}{x} (l o g \frac{y}{x} + 1)

Put

y = v x \Rightarrow \frac{d y}{d x} = v + x \frac{d v}{d x}

∴ v + x \frac{d v}{d x} = v l o g v + v \Rightarrow \frac{1}{v l o g v} d v = \frac{1}{x} d x \Rightarrow \int \frac{1}{v l o g v} d v = \int \frac{1}{x} d x \Rightarrow l o g (l o g v) = l o g x + l o g c

\Rightarrow l o g \frac{y}{x} = c x

Was this answer helpful ?

Next Question

Submit Solution

More Questions on This Topic :

Question 1. The degree and order of the differential equation of the family of all parabolas whose axis is x–axis, are respec....family of all parabolas whose axis is x–axis, are respectively

Question 2. The solution of dydx=yx+tanyx is....

Question 3. If y1(x) is a solution of the differential equation dydx−f(x)y=0, then a solution of the differential e....differential equation dydx−f(x)y=0, then a solution of the differential equation dydx+f(x)y=r(x)

Question 4. Solution of the equation xdy=(y+xf(yx)f′(yx))dx....

Question 5. The family of curves passing through (0,0) and satisfying the differential equation y2y1=1 (where yn=dnydxn) is ....

Question 6. S1: The differential equation of parabolas having their vertices at the origin and foci on the x-axis is an equation who....the axes of coordinates is an equation of order 2

Question 7. The general solution of the differential equation dydx=y tan x−y2sec x is....

Question 8. Solution to the differential equation x+x33!+x55!+.....1+x22!+x44!+.....=dx−dydx+dy is ....

Question 9. A curve is such that the mid point of the portion of the tangent intercepted between the point where the tangent is draw....the curve passes through (1, 0), then the curve is

Question 10. The solution of the differential equation (1+y2)+(x−etan−1y)dydx=0, is....

Chapter 1 - GLOBAL STEEL SCENARIO & INDIAN STEEL INDUSTRY Part 1 : (13-04-2024) INDUSTRY AND COMPANY AWARENESS (ICA)

Direction Sense Test Part 1 Reasoning (Hindi)

Chapter 1 - RMHP / OHP / OB & BP Part 1 : (14-02-2024) GPOE

Cube & Cuboid Part 1 Reasoning (Hindi)

Data Interpretation (DI) Basic Concept Reasoning (Hindi)

Counting Figures Part 1 Counting Of Straight Lines Reasoning (Hindi)

Sail E0 free webinar Webinars

Real Numbers Part 7 Class 10 Maths

Real Numbers Part 1 Class 10 Maths

Polynomials Part 1 Class 10 Maths

Pie Chart - Test Paper 1 Data Interpretation Reasoning & DI

Tabulation - Test Paper 2 Data Interpretation Reasoning & DI

Test Paper 1 Direction Sense Test Reasoning & DI

ICA , RDIC,GFM Free Modal Test Paper - Non - Technical Branch Old Syllabus 2022 - SAIL Junior Officer E0

GFM Combined 1 Free Revision Test SAIL JO E-0