WBJEE · Maths · Differential Equations
The integrating factor of the differential equation \(\left(1+x^{2}\right) \frac{d y}{d x}+y=e^{\tan ^{-1} x}\) is
- A \(\tan ^{-1} x\)
- B \(1+x^{2}\)
- C \(e^{\tan -1 x}\)
- D \(\log \left(1+x^{2}\right)\)
Answer & Solution
Correct Answer
(C) \(e^{\tan -1 x}\)
Step-by-step Solution
Detailed explanation
Given equation is \[ \left(1+x^{2}\right) \frac{d y}{d x}+y=e^{\tan ^{-1} x} \] or it can be rewritten as \[ \frac{d y}{d x}+\frac{1}{\left(1+x^{2}\right)} y=\frac{e^{\tan ^{-1} x}}{1+x^{2}} \] It is a linear differential equation of the form of \[ \frac{d y}{d x}+P y=Q \]…
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
- Number of solutions of the equation \(\tan x+\sec x=2 \cos x, x \in[0, \pi]\) isWBJEE 2012 Medium
- On set \(A=\{1,2,3\},\) relations \(R\) and \(S\) are given by \(R=\{(1,1),(2,2),(3,3),(1,2),(2,1)\}\)
\(S=\{(1,1),(2,2),(3,3),(1,3),(3,1)\}\)
Then,WBJEE 2017 Easy - The side \(A B\) of \(\triangle A B C\) is fixed and is of length \(2 a\) unit. The vertex moves in the plane such that the vertical angle is always constant and is \(\alpha\). Let \(x\)-axis be along \(A B\) and the origin be at \(A\). Then the locus of the vertex isWBJEE 2022 Hard
- \(\lim _{x \rightarrow 0^{+}}\left(e^{x}+x\right)^{1 / x}\)WBJEE 2019 Medium
- Let \(P\) be the set of all non-singular matrices of order 3 over \(R\) and \(Q\) be the set of all orthogonal matrices of order 3 over \(R .\) Then,WBJEE 2017 Easy
- If \(I=\int_{0}^{2} e^{x^{4}}(x-a) d x=0\), then \(\alpha\) lies in the intervalWBJEE 2014 Medium
More PYQs from WBJEE
- Let \((1+x)^{10}=\sum_{r=0}^{10} c_{r} x^{r}\) and \((1+x)^{7}=\sum_{r=0}^{7} d_{r} x^{r}\)
If \(P=\sum_{r=0}^{5} c_{2}\) and \(Q=\sum_{r=0}^{3} d_{2 r+1},\) then \(\frac{P}{Q}\) is equal
toWBJEE 2012 Medium - The number of possible organobromine compounds which can be obtained in the allylic bromination of 1 -butene with N-bromosuccinimide isWBJEE 2018 Easy
- A current \(I=I_{0} e^{-\lambda t}\) is flowing in a circuit consisting of a parallel combination of resistance \(R\) and capacitance \(C\). The total charge over the entire pulse period isWBJEE 2016 Hard
- The area of the region, bounded by the curves \(y=\sin ^{-1} x+x(1-x)\) and
\(y=\sin ^{-1} x-x(1-x)\) in the first quadrant, isWBJEE 2012 Medium - Let \(f(x)=x^{4}-4 x^{3}+4 x^{2}+c, c \in R .\) Then,WBJEE 2019 Medium
- The system of linear equations \(\lambda x+y+z=3\)
\(x-y-2 z=6\)
\(-x+y+z=\mu\) hasWBJEE 2012 Easy