Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa

Let \mathrm{ y=y_1(x) \: and\: y=y_2(x)} be the solution curves of the differential equation \mathrm{\frac{d y}{d x}=y+7} with initial conditions \mathrm{y_1(0)=0 \: and \: y_2(0)=1} respectively. Then the curves \mathrm{y=y_1(x)\: and \: y=y_2(x)} intersect at
 

Option: 1

no point

 


Option: 2

infinite number of points
 


Option: 3

one point
 


Option: 4

two points
 


Answers (1)

best_answer

\begin{aligned} & \frac{d y}{d x}=y+7 \Rightarrow \frac{d y}{d x}-y=7 \\ \end{aligned}

\begin{aligned} & \text { I.F. }=e^{-x} \\ \end{aligned}

\begin{aligned} & y e^{-x}=\int 7 e^{-x} d x \\ \end{aligned}

\begin{aligned} & \Rightarrow y e^{-x}=-7 e^{-x}+c \\ \end{aligned}

\begin{aligned} & \Rightarrow y=-7+c e^x \\ & -7+7 e^x=-7+8 e^x \Rightarrow e^x=0 . \end{aligned}
No solution

Posted by

manish

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: BTech CSE cut-offs for PwD candidates at NITs make entry easy; top institutes still selective
anam-khan

73 or 99 percentile? JEE Main result questioned, J-K candidate says, ‘Don’t create hype’
anam-khan

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

Latest Question