WBJEE · Maths · Differential Equations
The solution of the differential equation \(\left(y^{2}+2 x\right) \frac{d y}{d x}=y\) satisfies \(x=1, y=1\). Then the solution is
- A \(x=y^{2}\left(1+\log _{e} y\right)\)
- B \(y=x^{2}\left(1+\log _{e} x\right)\)
- C \(x=y^{2}\left(1-\log _{e} y\right)\)
- D \(y=x^{2}\left(1-\log _{e} x\right)\)
Answer & Solution
Correct Answer
(A) \(x=y^{2}\left(1+\log _{e} y\right)\)
Step-by-step Solution
Detailed explanation
Given differential equation is \(\left(y^{2}+2 x\right) \frac{d y}{d x}=y \Rightarrow \frac{d x}{d y}=\left(\frac{y^{2}+2 x}{y}\right)\) \(\Rightarrow \quad \frac{d x}{d y}=y+\frac{2 x}{y}\) \(\Rightarrow \quad \frac{d x}{d y}-\frac{2}{y} \cdot x=y\)…
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
- If \(X\) is a random variable such that \(\sigma(X)=2.6\) then \(\sigma(1-4 x)\) is equal toWBJEE 2019 Easy
- Let \(x-y=0\) and \(x+y=1\) be two perpendicular diameters of a circle of radius \(R\). The circle will pass through the origin if \(R\) is equal toWBJEE 2025 Medium
- Let \(S_{n}=\cot ^{-1} 2+\cot ^{-1} 8+\cot ^{-1} 18+\cot ^{-1} 32+\ldots \ldots .\) to \(n^{\text {th }}\) term. Then \(\lim _{n \rightarrow \infty} S_{n}\) isWBJEE 2021 Easy
- 4 boys and 2 girls occupy seats in a row at random. Then the probability that the two girls occupy seats side by side isWBJEE 2011 Hard
- If the four points with position vectors \(-2\hat i+\hat j + \hat k, \hat i+\hat j+\hat k,\hat j- \hat k\) and \(\lambda \hat j + \hat k\) are coplanar, then \(\lambda\) is equal toWBJEE 2015 Easy
- If the relation between the direction ratios of two lines in \(\mathbb{R}^3\) are given by \(l+m+n=0,2 / m+2 m n-l n=0\) then the angle between the lines is ( \(I, m\), \(n\) have their usual meaning)WBJEE 2024 Easy
More PYQs from WBJEE
- If \(F(x)=\int_{0}^{x} \frac{\cos t}{\left(1+t^{2}\right)} d t, 0 \leq x \leq 2 \pi .\) ThenWBJEE 2013 Medium
- The value of \(\int_{-100}^{100} \frac{\left(x+x^3+x^5\right)}{\left(1+x^2+x^4+x^6\right)} d x\) isWBJEE 2025 Easy
- The velocity of sound in air at \(20^{\circ} \mathrm{C}\) and 1 atm pressure is \(344.2 \mathrm{m} / \mathrm{s}\). At \(40^{\circ} \mathrm{C}\) and \(2 \mathrm{atm}\)
pressure, the velocity of sound in air is approximatelyWBJEE 2016 Medium - Let \(\alpha, \beta\) be the roots of \(x^{2}-x-1=0\) and \(S_{n}=\alpha^{n}+\beta^{n},\) for all integers \(n \geq 1 .\) Then, for every integer \(n \geq 2\)WBJEE 2014 Medium
- Let \(y=\left(\frac{3^{x}-1}{3^{x}+1}\right) \sin x+\log _{e}(1+x) \quad x>-1\) Then, at \(x=0, \frac{d y}{d x}\) equalsWBJEE 2012 Hard
- A straight line through the origin \(\mathrm{O}\) meets the parallel lines \(4 \mathrm{x}+2 \mathrm{y}=9\) and \(2 \mathrm{x}+\mathrm{y}+6=0\) at \(\mathrm{P}\) and \(\mathrm{Q}\) respectively. The point O divides the segment \(\mathrm{PQ}\) in the ratioWBJEE 2020 Easy