MHT CET · Maths · Differential Equations
The differential equation, having general solution as \(\mathrm{A} x^2+\mathrm{B} y^2=1\), where A and B are arbitrary constants, is
- A \(x y \frac{\mathrm{~d}^2 y}{\mathrm{~d} x^2}-x\left(\frac{\mathrm{~d} y}{\mathrm{~d} x}\right)^2-y \frac{\mathrm{~d} y}{\mathrm{~d} x}=0\)
- B \(x y \frac{\mathrm{~d}^2 y}{\mathrm{~d} x^2}-x\left(\frac{\mathrm{~d} y}{\mathrm{~d} x}\right)^2+y \frac{\mathrm{~d} y}{\mathrm{~d} x}=0\)
- C \(x y \frac{\mathrm{~d}^2 y}{\mathrm{~d} x^2}+x\left(\frac{\mathrm{~d} y}{\mathrm{~d} x}\right)^2+y \frac{\mathrm{~d} y}{\mathrm{~d} x}=0\)
- D \(x y \frac{\mathrm{~d}^2 y}{\mathrm{~d} x^2}+x\left(\frac{\mathrm{~d} y}{\mathrm{~d} x}\right)^2-y \frac{\mathrm{~d} y}{\mathrm{~d} x}=0\)
Answer & Solution
Correct Answer
(D) \(x y \frac{\mathrm{~d}^2 y}{\mathrm{~d} x^2}+x\left(\frac{\mathrm{~d} y}{\mathrm{~d} x}\right)^2-y \frac{\mathrm{~d} y}{\mathrm{~d} x}=0\)
Step-by-step Solution
Detailed explanation
\(\mathrm{A} x^2+\mathrm{B} y^2=1\)
Differentiating w.r.t. \(x\), we get
\(2 \mathrm{~A} x+2 \mathrm{~B} y \frac{\mathrm{~d} y}{\mathrm{~d} x}=0...(i)\)
Again, differentiating w.r.t. \(x\), we get
\(2 \mathrm{~A}+2 \mathrm{~B}\left[\left(\frac{\mathrm{~d} y}{\mathrm{~d} x}\right)^2+y \frac{\mathrm{~d}^2 y}{\mathrm{~d} x^2}\right]=0...(ii)\)
Solving (i) and (ii), we get
\(x y \frac{\mathrm{~d}^2 y}{\mathrm{~d} x^2}+x\left(\frac{\mathrm{~d} y}{\mathrm{~d} x}\right)^2-y \frac{\mathrm{~d} y}{\mathrm{~d} x}=0\)
Differentiating w.r.t. \(x\), we get
\(2 \mathrm{~A} x+2 \mathrm{~B} y \frac{\mathrm{~d} y}{\mathrm{~d} x}=0...(i)\)
Again, differentiating w.r.t. \(x\), we get
\(2 \mathrm{~A}+2 \mathrm{~B}\left[\left(\frac{\mathrm{~d} y}{\mathrm{~d} x}\right)^2+y \frac{\mathrm{~d}^2 y}{\mathrm{~d} x^2}\right]=0...(ii)\)
Solving (i) and (ii), we get
\(x y \frac{\mathrm{~d}^2 y}{\mathrm{~d} x^2}+x\left(\frac{\mathrm{~d} y}{\mathrm{~d} x}\right)^2-y \frac{\mathrm{~d} y}{\mathrm{~d} x}=0\)
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
\(\int(7 x-2) \sqrt{3 x+2} \mathrm{~d} x=\mathrm{A}(3 x+2)^{\frac{5}{2}}+\mathrm{B}(3 x+2)^{\frac{3}{2}}+\mathrm{c}\)
(where c is a constant of integration), then the values of \(A\) and \(B\) are respectivelyMHT CET 2024 Easy - The shaded figure given below is the solution set for the linear inequations. Choose the correct option
MHT CET 2021 Easy - Equation of the plane passing through \((-2,2,2)\) and \((2,-2,-2)\) and perpendicular to the plane \(9 x-13 y-3 z=0\) isMHT CET 2009 Easy
- If \(2 a+b+3 c=0\), then the line \(a x+b y+c=0\) passes through the fixed point that isMHT CET 2012 Easy
- If \(\bar{a}=(2 \hat{i}+2 \hat{j}+3 \hat{k}), \bar{b}=(-\hat{i}+2 \hat{j}+\hat{k}) \quad\) and \(\overline{\mathrm{c}}=(3 \hat{\mathrm{i}}+\hat{\mathrm{j}})\) such that \((\overline{\mathrm{a}}+\lambda \overline{\mathrm{b}})\) is perpendicular to \(\bar{c}\), then the value of \(\lambda\) isMHT CET 2024 Medium
- The equation of the plane containing the line \(\frac{x+1}{-3}=\frac{y-3}{2}=\frac{z+2}{1}\) and the point \((0,7,-7)\) isMHT CET 2008 Easy
More PYQs from MHT CET
- The work done in blowing a soap bubble of radius \(R\) is \(W_1\) and that of radius \(2 R\) is \(W_2\). The ratio of \(W_1\) to \(W_2\) isMHT CET 2022 Medium
- If and are foot of perpendicular drawn from point to the planes and , then equation of plane through the points and is _______MHT CET 2016 Medium
- A gas absorbs \(150 \mathrm{~J}\) heat and expands by \(300 \mathrm{~cm}^3\) against a constant external pressure \(2 \times 10^5 \mathrm{~N} \mathrm{~m}^{-2}\), What is \(\Delta \mathrm{U}\) of the system?MHT CET 2023 Medium
- A long solenoid has 1500 turns. When a current of \(3.5 \mathrm{~A}\) flows through it, the magnetic flux linked with each turn of solenoid is \(2.8 \times 10^{-3}\) weber. The self-inductance of solenoid isMHT CET 2023 Medium
- How many statement from the following are correct?
(a) In plants, phosphorylation occurs by three different ways.
(b) Substrate level phosphorylation is a direct phosphorylation of ADP by transfer of a phosphate group from any suitable substance.
(c) Substrate level phosphorylation occurs cytoplasm of cell only.
(d) Oxidative phosphorylation occurs on the inner mitochondrial membrane only.MHT CET 2022 Medium - If \(M_0\) and \(L_0\) denote the magnetic moment and angular momentum of the electron due to its orbital motion respectively, then the gyromagnetic ratio is given byMHT CET 2022 Easy