COMEDK · Maths · 32. Differential Equations
The order and degree of the differential equation \(\left(\dfrac{dy}{dx}\right)^2 + \dfrac{dx}{dy} = x\) is:
- A \((1, 1)\)
- B \((1, 2)\)
- C \((1, 3)\)
- D \((2, 1)\)
Answer & Solution
Correct Answer
(C) \((1, 3)\)
Step-by-step Solution
Detailed explanation
The given differential equation is \(\left(\dfrac{dy}{dx}\right)^2 + \dfrac{dx}{dy} = x\). We know that \(\dfrac{dx}{dy} = \dfrac{1}{\dfrac{dy}{dx}}\). Substituting this in the given equation, we get: \(\left(\dfrac{dy}{dx}\right)^2 + \dfrac{1}{\dfrac{dy}{dx}} = x\) Multiplying…
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 approximate value of \((0.026)^{\overline{3}}\) isCOMEDK 2024 Easy
- If \(f:[0, \infty) \rightarrow[2, \infty)\) is given by \(f(x)=x+\frac{1}{x}\), then \(f^{-1}(x)\) equalsCOMEDK 2014 Easy
- The expression \(\dfrac{\tan\left(x - \dfrac{\pi}{2}\right)\cos\left(\dfrac{3\pi}{2} + x\right) - \sin^3\left(\dfrac{7\pi}{2} - x\right)}{\cos\left(x - \dfrac{\pi}{2}\right)\tan\left(\dfrac{3\pi}{2} + x\right)}\) simplifies to:COMEDK 2026 Easy
- An unbiased die is tossed twice. What is the probability of getting a 4,5 or 6 on the first toss and a 1,2,3 or 4 on the second toss?COMEDK 2025 Medium
- If \(|\mathbf{a}|=2,|\mathbf{b}|=7\) and \(\mathbf{a} \times \mathbf{b}=3 \hat{\mathbf{i}}+2 \hat{\mathbf{j}}+6 \hat{\mathbf{k}}\), then the angle between and \(b\) isCOMEDK 2012 Easy
- The value of \(\lim _{x \rightarrow 0} \frac{5^{x}-5^{-x}}{2 x}=\)COMEDK 2016 Easy
More PYQs from COMEDK
- The concentration of a reactant \(X\) decreases from 0.1 \(\mathrm{M}\) to \(0.025 \mathrm{M}\) in \(40 \mathrm{~min}\). If the reaction follows I order kinetics, the rate of the reaction when the concentration of \(X\) is \(0.01 \mathrm{M}\) will beCOMEDK 2018 Medium
- A regular hexagon of side \(m\) which is a wire of length \(24 \mathrm{~m}\) is coiled on that hexagon. If current in hexagon is \(I\), then the magnetic moment,
COMEDK 2022 Easy - In the group \(G=\{1,5,7,11\}\) under \(\otimes_{12}\) the value of \(7 \otimes_{12} 1 \hat{l}^{-1}\) is equal toCOMEDK 2012 Medium
- Codes used for vehicle identification consists of two distinct English alphabets followed by two distinct digits from 1 to 9 . How many of them end with an even number.COMEDK 2025 Medium
- \(\int \dfrac{4^x}{\sqrt{1-16^x}} d x\) is equal toCOMEDK 2023 Medium
- The order of the differential equation \(\dfrac{d}{d x}\left[\left(\dfrac{d y}{d x}\right)^3\right]=0\) isCOMEDK 2025 Easy