AP EAMCET · Maths · Differential Equations
If \(x d y+\left(y+y^2 x\right) d x=0\) and \(y=1\) at \(x=1\). then
- A \(y=\frac{x}{1+\log x}\)
- B \(y=\frac{1+\log x}{x}\)
- C \(y=x(1+\log x)\)
- D \(y=\frac{1}{x(1+\log x)}\)
Answer & Solution
Correct Answer
(D) \(y=\frac{1}{x(1+\log x)}\)
Step-by-step Solution
Detailed explanation
Since, \(x d y+\left(y+y^2 x\right) d x=0\) \(\Rightarrow \frac{d y}{d x}+\frac{y}{x}+y^2=0...(i)\) Let \(y=\frac{1}{t} \Rightarrow \frac{d y}{d x}=-\frac{1}{t^2} \frac{d t}{d x}\)…
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
- Let \(\mathbf{a}=\mathbf{i}+2 \mathbf{j}+\mathbf{k}, \mathbf{b}=\mathbf{i}-\mathbf{j}+\mathbf{k}, \mathbf{c}=\mathbf{i}+\mathbf{j}-\mathbf{k}\). A vector in the plane of \(\mathbf{a}\) and \(\mathbf{b}\) has projection \(\frac{1}{\sqrt{3}}\) on c. Then, one such vector isAP EAMCET 2012 Easy
- Which statement among the following is true?
(i) The function is strictly increasing on .
(ii) The function is strictly increasing on .
(iii) A one-one function is always an increasing function.
(iv) is strictly decreasing onAP EAMCET 2021 Medium - \(\begin{aligned}
& \frac{4 x^2+5}{(x-2)^4}=\frac{A}{(x-2)}+\frac{B}{(X-2)^2}+\frac{C}{(X-2)^3}+\frac{D}{(X-2)^4} \text { then } \\
& \sqrt{\frac{A}{C}+\frac{B}{C}+\frac{D}{C}}=
\end{aligned}\)AP EAMCET 2024 Easy - If \(f(x)=x e^{x(1-x)}, x \in \mathbb{R}\), then \(f(x)\) isAP EAMCET 2025 Medium
- If is a pentagon, then the resultant of forces and isAP EAMCET 2020 Medium
- \(\frac{1}{1.5}+\frac{1}{5.9}+\frac{1}{9.13}+\ldots\) upto \(n\) terms \(=\)AP EAMCET 2024 Easy
More PYQs from AP EAMCET
- The following data is obtained for coagulating a positively charged sol in 2 hours
\(\begin{array}{|c|l|}\hline \text{Conc. of } \mathrm{Cl}^{-} \text{ in } \mathrm{mol} \mathrm{L}^{-1} & \text{ Result } \\ \hline 5 \times 10^{-5} & \text{Sol not precipitated} \\ \hline 6 \times 10^{-5} & \text{Sol not precipitated} \\ \hline 7 \times 10^{-5} & \text{Sol precipitated} \\ \hline 8 \times 10^{-5} & \text{Sol precipitated} \\ \hline 1 \times 10^{-4} & \text{Sol precipitated} \\ \hline\end{array}\)
What is the coagulating value of electrolyte for this sol?AP EAMCET 2024 Medium - The circumcentre of the triangle formed by the points \((1,2,3),(3,-1,5),(4,0,-3)\) isAP EAMCET 2017 Medium
- Two wooden blocks of masses \(M\) and \(m\) are placed on a smooth horizontal surface as shown in figure. If a force \(P\) is applied to the system as shown in figure such that the mass \(m\) remains stationary with respect to block of mass \(M\), then the magnitude of the force \(P\) is
AP EAMCET 2013 Medium - If \(r=\) in radius, \(\triangle=\) Area of \(\triangle A B C, s=\) semi-perimeter then which of the following is true?AP EAMCET 2020 Medium
- Let \(\mathbf{a}, \mathbf{b}\) and \(\mathbf{c}\) be unit vectors such that \(\mathbf{a} \cdot \mathbf{b}=0=\mathbf{a} \cdot \mathbf{c}\) and the acute angle between \(\mathbf{b}\) and \(\mathbf{c}\) is \(\frac{\pi}{3}\), then \(|\mathbf{a} \times \mathbf{b}-\mathbf{a} \times \mathbf{c}|\) is equal toAP EAMCET 2021 Easy
- Which air pollutant is responsible for Bhopal gas tragedy?AP EAMCET 2011 Easy