Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
BITSAT 2023Paper 1
Exam
BITSAT
Year
2023
Paper
Paper 1
Subject
Mathematics
Chapter
Differential Equations

BITSAT 2023 · Paper 1 · Mathematics · Differential Equations

The number of solutions of (d y)/(d x)=(y+1)/(x-1) , when y(1)=2 is

The number of solutions of dydx=y+1x−1\frac{d y}{d x}=\frac{y+1}{x-1}, when y(1)=2y(1)=2 is

Options

  1. Anone
  2. Bone
  3. Ctwo
  4. Dinfinite

Correct answer

B. one

Step-by-step solution

Since, dydx=y+1x−1\frac{d y}{d x}=\frac{y+1}{x-1}
⇒dyy+1=dxx−1\Rightarrow \quad \frac{d y}{y+1}=\frac{d x}{x-1}
After integrating on both sides, we have
log⁡(y+1)=log⁡(x−1)−log⁡C\log (y+1)=\log (x-1)-\log C
C(y+1)=(x−1)C(y+1)=(x-1)
C=x−1y+1C=\frac{x-1}{y+1}
If x=1x=1, then y=2y=2, so C=0C=0
Therefore, x−1=0x-1=0
Hence, there is only one solution.
Practice Differential Equations on Quantrex Academy →

More from Differential Equations

The solution of the differential equation (x+1) (d y)/(d x)-y=e^ 3 x (x+1)^2 is BITSAT 2024If (d y)/(d x)-y _e 2=2^ x ( x-1) _e 2 , then y BITSAT 2024The integrating factor of (x d y)/(d x)-y=x^4-3 x is BITSAT 2023((d y)/(d x)) x=y ^2 x+ x , find general solution BITSAT 2022If the slope of the tangent to the curve at any point P(x, y) is (y)/(x)- ^ 2 (y)/(x)… BITSAT 2021The general solution of the differential equation ( ^ -1 y-x) d y=(1+y^ 2 ) d x is BITSAT 2021The solution of the differential equation (x+1) (d y)/(d x)-y=e^ 3 x (x+1)^ 2 is BITSAT 2020The solutions of (x+y+1) d y=d x are BITSAT 2020Solution of the equation (dy)/(dx) = e^ x - y (e^ x - e^ y ) is BITSAT 2019If f^ ' (x) = f(x) + ∫ _ 0 ^ 1 f(x)dx, f(0) = 1 , then f(x) = BITSAT 2019Solution of the differential equation (dy)/(dx) = (x + y) + (x + y) is equal to BITSAT 2018The equation of the curve whose slope at any point is equal to y + 2x and which passes… BITSAT 2018The solution of the differential equation d^ 2 y dx^ 2 = 3x + e^ x + x^ 2 when y _ 1 (0)… BITSAT 2018The solution of (dy)/(dx) = (x + y) + (x + y), is BITSAT 2017For any differentiable function y of x , d^ 2 x d y^ 2 ((d y)/(d x))^ 3 + d^ 2 y d x^ 2 = BITSAT 2016If φ(x) is a differential function, then the solution of the differential equation dy+\ y… BITSAT 2015 Full Differential Equations list Differential Equations JEE Maths PYQsJEE Mathematics PYQs All BITSAT PYQs