Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Engineering
  • Let  be the solution of the differential equation   <img alt="(x+1) y^{\prime}-y=e^{3 x}(x

Let y=y(x) be the solution of the differential equation   (x+1) y^{\prime}-y=e^{3 x}(x+1)^{2}, with y(0)=\frac{1}{3}. Then, the point x=-\frac{4}{3} for the curve y=y(x) \text { is : }

Option: 1

not a critical point


Option: 2

a point of local minima


Option: 3

a point of local maxima


Option: 4

a point of inflection


Answers (1)

best_answer

\mathrm{\left ( x+1 \right )dy-y\, dx= e^{3x}\left ( x+1 \right )^{2}}

\mathrm{\frac{\left ( x+1 \right )dy-y\, dx}{\left ( x+1 \right )^{2}}= e^{3x}}
\mathrm{d\left ( \frac{y}{x+1} \right )= d(e^{3x})\; \Rightarrow \; \frac{y}{x+1}= \frac{e^{3x}}{3}+c}
\\\mathrm{\left ( 0,\frac{1}{3}\right )\Rightarrow c= 0\; \\ \Rightarrow \: y= \frac{\left ( x+1 \right )e^{3x}}{3} }

\mathrm{\frac{dy}{dx} = \frac{1}{3}\left ( \left ( x+1 \right )3e^{3x}+e^{3x} \right )= \frac{e^{3x}}{3}\left ( 3x+4 \right )}

At x = -4/3, f'(x) changes sign from negative to positive
Hence , \mathrm{x= -4/3} is point of local minima.

Posted by

Nehul

View full answer

JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE

Similar Questions

Trending Articles/News

anam-khan

JEE Main 2025: 11 from Kota coaching centres among 24 students with 100 percentile
anam-khan

Low JEE Main rank? Explore alternative paths for engineering admission
anam-khan

Gender-gap in JEE Main 2025: Female participation remains around 31%, overall pool drops by 7.09%

Latest Question