WBJEE · Maths · Differential Equations
Let \(y(x)\) be a solution of \(\left(1+x^{2}\right) \frac{d y}{d x}+2 x y-4 x^{2}=0\) and \(y(0)=-1 .\) Then y(1) s equal to
- A \(\frac{1}{2}\)
- B \(\frac{1}{3}\)
- C \(\frac{1}{6}\)
- D 1
Answer & Solution
Correct Answer
(C) \(\frac{1}{6}\)
Step-by-step Solution
Detailed explanation
We have. \(\left(1+x^{2}\right) \frac{d y}{d x}+2 x y-4 x^{2}=0\) \(\Rightarrow \quad \frac{d y}{d x}+\left(\frac{2 x}{1+x^{2}}\right) y=\frac{4 x^{2}}{1+x^{2}}\) Here. \(\mathrm{IF}=e^{\frac{1}{1+x^{2}}}=e^{\log \left(1+x^{2}\right)}=1+x^{2}\)…
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
- For the variable \(t,\) the locus of the points of intersection of lines \(x-2 y=t\) and \(x+2 y=\frac{1}{t}\) isWBJEE 2013 Medium
- If \(a, b, c\) are in G.P. \((a>1, b>1, c>1)\), then for any real number \(x(\) with \(x>0, x \neq 1), \log _{\mathrm{a}} x, \log _{\mathrm{b}} x, \log _{\mathrm{c}} x\) are inWBJEE 2009 Hard
- \(\int \frac{x^{2}-1}{x^{4}+3 x^{2}+1} d x(x>0)\) isWBJEE 2017 Hard
- Simplest form of \(\frac{2}{\sqrt{2+\sqrt{2+\sqrt{2+2 \cos 4 x}}}}\) isWBJEE 2009 Hard
- The probability that at least one of \(A\) and \(B\) occurs is 0.6 . If A and \(B\) occur simultaneously with probability 0.3 , then \(P^{\prime}\left(A^{\prime}\right)+P_{(}\left(B^{\prime}\right)\) isWBJEE 2010 Medium
- In order to get a head at least once with probability \(\geq 0.9\), the minimum number of times a unbiased coin needs to be tossed isWBJEE 2018 Medium
More PYQs from WBJEE
- In a group of 14 males and 6 females. 8 and 3 of the males and females, respectively are aged above 40 yr. The probability that a selected at random from the group is person aged above \(40 \mathrm{yr}\) given that the selected person is a female, isWBJEE 2016 Medium
- The magnetic field at the point of intersection of diagonals of a square wire loop of side \(\mathrm{L}\) carrying a current \(\mathrm{I}\) isWBJEE 2011 Hard
- \(A\) 10 W electric heater is used to heat a container filled with \(0.5 \mathrm{kg}\) of water. It is found that the temperature of water and the container rises by \(3^{\circ} \mathrm{K}\) in \(15 \mathrm{min}\). The container is then emptied, dried and filled with \(2 \mathrm{kg}\) of oil. The same heater now raises the temperature of container-oil system by \(2^{\circ} \mathrm{K}\) in \(20 \mathrm{min}\). Assuming that there is no heat loss in the process and the specific heat of water is \(4200 \mathrm{d} \mathrm{kg}^{-1} \mathrm{K}^{-1}\), the specific heat of oil in the same unit is equal toWBJEE 2014 Hard
- When a spring is stretched by \(10 \mathrm{cm}\), the potential energy stored is \(E\). When the spring is stretched by \(10 \mathrm{cm}\) more, the potential energy stored in the spring becomesWBJEE 2012 Easy
- The equivalent weight of \(\mathrm{KIO}_3\) in the given reaction is (\(\mathrm{M}=\) molecular mass) :
\(2 \mathrm{Cr}(\mathrm{OH})_3+4 \mathrm{OH}^{-}+\mathrm{KIO}_3 \rightarrow 2 \mathrm{CrO}_4{ }^{2-}+5 \mathrm{H}_2 \mathrm{O}+\mathrm{KI}\)WBJEE 2023 Easy - Given \(\frac{d^2 y}{d x^2}+\cot x \frac{d y}{d x}+4 y \operatorname{cosec}^2 x=0\). Changing the independent variable \(x\) to \(z\) by the substitution \(z=\log \tan \frac{x}{2}\), the equation is changed toWBJEE 2023 Hard