AP EAMCET · Maths · Differential Equations
The solution of \(\left(1+y^2\right) d x-x y d y=0, y(1)=0\) represents a conic. Its eccentricity is
- A 2
- B \(1 / \mathrm{e}\)
- C 1
- D \(\sqrt{2}\)
Answer & Solution
Correct Answer
(D) \(\sqrt{2}\)
Step-by-step Solution
Detailed explanation
Given \(\left(1+y^2\right) d x-x y d y-0\) and \(y(1)=0\). Take, \(\left(1+y^2\right) d x-x y d y=0\) \[ d x\left(1+y^2\right)=x y d y \] \[ \int \frac{d x}{x}=\int \frac{y d y}{d+y^2} \]…
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
- The locus of a point which moves such that the area of the triangle formed by it with the vertices \((1,2)\) and \((-2,5)\) is 8 sq. units is/areAP EAMCET 2020 Easy
- If \(z=(1-i)^3(x+i)\) is a purely imaginary number for \(x=x_1\) and if \(\mathrm{z}\) is a purely real number for \(\mathrm{x}=\mathrm{x}_2\), then \(\mathrm{x}_1 \mathrm{x}_2=\)AP EAMCET 2023 Easy
- The polar of \((1,-2)\) with respect to \(x^2+y^2-10 x-10 y+25=0\) isAP EAMCET 2020 Medium
- The values of \(a\) and \(b\) for which the function
\(f(x)=\left\{\begin{array}{cc}
1+|\sin x|^{a/|\sin x|}, & \frac{-\pi}{6} \lt x \lt 0 \\
b, & x=0 \\
e^{\tan 2 x / \tan 3 x}, & 0 \lt x \lt \frac{\pi}{6}
\end{array}\right.\)
is continuous at \(x=0\) areAP EAMCET 2024 Hard - The solution of the differential equation \(\frac{d y}{d x}=\frac{x-2 y+1}{2 x-4 y}\) isAP EAMCET 2008 Hard
- If \(\left[\begin{array}{ccc}1 & -1 & x \\ 1 & x & 1 \\ x & -1 & 1\end{array}\right]\) has no inverse, then the real value of \(x\) isAP EAMCET 2020 Easy
More PYQs from AP EAMCET
- The de Broglie wavelength associated with an electron accelerated through a potential difference of \(\frac{200}{3} \mathrm{~V}\) is nearlyAP EAMCET 2025 Medium
- Choose the correct option regarding the following statements
1. \(C_0+C_2+C_4+\ldots+C_n=2^{n-1}\), if \(n\) is even
2. \(C_1+C_3+C_5+\ldots+C_{n-1}=2^{n-1}\), if \(n\) is evenAP EAMCET 2020 Medium - The number of ways of dividing 200 dissimilar things into 10 groups each containing 20 elements isAP EAMCET 2022 Medium
- If the average translational kinetic energy of a molecule in a gas is equal to the kinetic energy of an electron accelerating from rest through \(10 \mathrm{~V}\), then the temperature of the gas molecule is
\[
\left(\text { Boltzmann constant }=1.38 \times 10^{-23} \mathrm{JK}^{-1}\right)
\]AP EAMCET 2017 Easy - If \(\mathrm{X}, \mathrm{Y}\) and Z are the sizes of the emitter, base and collector of a transistor respectively, thenAP EAMCET 2025 Easy
- Ethylene on reaction with Baeyer's reagent gives the compound \(\underline{\underline{A}}\). In the preparation of co-polymer X, compound A is used as monomer. What is X?AP EAMCET 2017 Easy