KCET · Maths · Differential Equations
The number of solutions of \(\frac{d y}{d x}=\frac{y+1}{x-1}\), when \(y(\mathrm{l})=2\) is
- A three
- B one
- C infinite
- D two
Answer & Solution
Correct Answer
(B) one
Step-by-step Solution
Detailed explanation
\(\frac{d y}{d x}=\frac{y+1}{x-1}\)
\(\Rightarrow \quad \frac{1}{x-1} d x=\frac{1}{y+1} d y\)
Integrating both sides,
\(\int \frac{1}{x-1} d x=\int \frac{1}{y+1} d y\)
\(\Rightarrow \quad \log |x-1|=\log |y+1|+\log C\)
\(\Rightarrow \quad(x-1)=c(y+1)\)
As, \(\quad y(1)=2\),
\(0=c(3)\)
\(\Rightarrow \quad c=0\)
Hence, \(x-1=0\) or \(x=1\)
The given differential equation has only one solution.
\(\Rightarrow \quad \frac{1}{x-1} d x=\frac{1}{y+1} d y\)
Integrating both sides,
\(\int \frac{1}{x-1} d x=\int \frac{1}{y+1} d y\)
\(\Rightarrow \quad \log |x-1|=\log |y+1|+\log C\)
\(\Rightarrow \quad(x-1)=c(y+1)\)
As, \(\quad y(1)=2\),
\(0=c(3)\)
\(\Rightarrow \quad c=0\)
Hence, \(x-1=0\) or \(x=1\)
The given differential equation has only one solution.
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- The differential equation \(y \frac{d y}{d x}+x=\) crepresentsKCET 2008 Medium
- \( \int \sqrt{x^{2}+2 x+5} d x \) is equal toKCET 2017 Medium
- \(f: R \rightarrow R\) defined by \(f(x)\) is equal to \(\left\{\begin{array}{c}2 x, x>3 \\ x^{2}, 1 < x \leq 3, \text { then } f(-2)+f(3)+f(4) \text { is } \\ 3 x, x \leq 1\end{array}\right.\)KCET 2021 Easy
- \(A\) and \(B\) are two sets having 3 and 6 elements respectively.
Consider the following statements.
Statement (I): Minimum number of elements in AUB is 3
Statement (II): Maximum number of elements in AB is 3
Which of the following is correct?KCET 2025 Easy - If \(y=2 x^{n+1}+\frac{3}{x^{n}}\), then \(x^{2} \frac{d^{2 y}}{d x^{2}}\) isKCET 2020 Easy
- For the curve \(4 x^{5}=5 y^{4}\), the ratio of the cube of the subtangent at a point on the curve the square of the subnormal at the same point isKCET 2010 Hard
More PYQs from KCET
- The middle term of expansion of \( \left(\frac{10}{x}+\frac{x}{10}\right)^{10} \)KCET 2015 Easy
- The embryo sac of an angiosperm is made up ofKCET 2013 Hard
- If \( x=a \cos ^{3} \theta, y=a \sin ^{3} \theta \), then \( 1+\left(\frac{d y}{d x}\right)^{2} \) isKCET 2015 Easy
- Identify the major site of biosynthesis of lipids.KCET 2018 Hard
- What amount of dioxygen (in gram) contains \( 1.8 \times 10^{22} \) molecules ?KCET 2015 Easy
- The value of \(\sin 10^{\circ} \cdot \sin 30^{\circ} \cdot \sin 50^{\circ} \cdot \sin 70^{\circ}\) isKCET 2011 Easy