AP EAMCET · Maths · Differential Equations
The solution of \(x \frac{d y}{d x}=y+x e^{y / x}\) with \(y(1)=0\) is
- A \(e^{y / x}+\log x=1\)
- B \(e^{-y / x}=\log x\)
- C \(e^{-y / x}+2 \log x=1\)
- D \(e^{-y / x}+\log x=1\)
Answer & Solution
Correct Answer
(D) \(e^{-y / x}+\log x=1\)
Step-by-step Solution
Detailed explanation
Given differential equation is \[ \begin{gathered} x \frac{d y}{d x}=y+x e^{y / x} \\ \frac{d y}{d x}=\frac{y}{x}+e^{y / x} \end{gathered} \] It is a homogeneous differential equation.…
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 \(\mathrm{P}\left(\frac{\pi}{4}\right)\) and \(\mathrm{Q}\left(\frac{3 \pi}{4}\right)\) are two points on the hyperbola \(4 x^2-y^2-8 x-2 y-13=0\) in parametric form, then the distance between \(\mathrm{P}\) and \(\mathrm{Q}\) isAP EAMCET 2023 Easy
- An equilateral triangle is inscribed in the parabola \(y^2=8 x\), with one of its vertices is the vertex of the parabola. Then, length of the side of that triangle isAP EAMCET 2015 Easy
- If the origin is shifted to remove the first degree terms from the equation \(2 x^2-3 y^2+4 x y+4 x+4 y-14=0\) then, with respect to this new co-ordinate system, the transformed equation of \(x^2+y^2-3 x y+4 y+3=0\) isAP EAMCET 2024 Medium
- If the velocity of a particle moving on a straight line is proportional to the cube root of its displacement, then its acceleration isAP EAMCET 2025 Medium
- \(\int_0^3\left|x^2-3 x+2\right| d x=\)AP EAMCET 2018 Medium
- \(\int\left[(\log 2 x)^2+2 \log 2 x\right] d x=\)AP EAMCET 2024 Easy
More PYQs from AP EAMCET
- The molecular geometry of \(\mathrm{PF}_3\) is ...... .AP EAMCET 2020 Easy
- If the coefficients of variation of two distributions are 60 and 70 and their standard deviations are 21 and 16 respectively, then their arithmetic means are respectivelyAP EAMCET 2017 Medium
- \(\operatorname{Sech}^{-1}(\sin \alpha)=\)AP EAMCET 2025 Medium
- A charge \(\mathrm{Q}\) is to be divided between two objects. The values of the charges on the objects so that the electrostatic force between them will be maximum isAP EAMCET 2022 Easy
- Find the absolute maximum of \(x^{40}-x^{20}\) on the interval \([0,1]\).AP EAMCET 2021 Hard
- Let \((\vec{a}, \vec{b})\) denote the angle between vectors \(\vec{a}\) and \(\vec{b}\). If \(\vec{a}=2 \hat{i}+3 \hat{j}+6 \hat{k}, \vec{a} \cdot \vec{b}=4\) and \((\vec{a}, \vec{b})=\cos ^{-1}\left(\frac{4}{21}\right)\), then \(\overline{\mathrm{a}}+\overline{\mathrm{b}}=\)AP EAMCET 2023 Easy