AP EAMCET · Maths · Differential Equations
The general solution of the differential equation \(\frac{d y}{d x}=\frac{2 x^2-x y-y^2}{x^2-y^2}\) is
- A \(\log \left|\frac{y^2-2 x^2}{x^2}\right|+\sqrt{2} \log \left|\frac{y-\sqrt{2} x}{y+\sqrt{2} x}\right|+2 \sqrt{2} \log |x|=c\)
- B \(\sqrt{2} \log \left|\frac{y^2-2 x^2}{x^2}\right|+\log \left|\frac{y-\sqrt{2} x}{y+\sqrt{2} x}\right|+2 \sqrt{2} \log |x|=c\)
- C \(\sqrt{2} \log \left|\frac{y^2+2 x^2}{x^2}\right|+\log \left|\frac{y+\sqrt{2} x}{y-\sqrt{2} x}\right|+2 \sqrt{2} \log |x|=c\)
- D \(\log \left|\frac{2 x^2-y^2}{x^2}\right|+\sqrt{2} \log \left|\frac{y+\sqrt{2} x}{y-\sqrt{2} x}\right|+\log |x|=c\)
Answer & Solution
Correct Answer
(B) \(\sqrt{2} \log \left|\frac{y^2-2 x^2}{x^2}\right|+\log \left|\frac{y-\sqrt{2} x}{y+\sqrt{2} x}\right|+2 \sqrt{2} \log |x|=c\)
Step-by-step Solution
Detailed explanation
NO SOLUTION
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 \(l_1=\lim _{x \rightarrow 2^{+}}(x+[x]), l_2 \lim _{x \rightarrow 2^{-}}(2 x-[x])\) and \(l_3=\lim _{x \rightarrow \pi / 2} \frac{\cos x}{(x-\pi / 2)}\), then :AP EAMCET 2006 Medium
- If the intercepts made by a variable circle on the X -axis and Y -axis are 8 and 6 units respectively, then the locus of the centre of the circle isAP EAMCET 2025 Medium
- If \(\cos ^3 80^{\circ}+\cos ^3 40^{\circ}-\cos ^3 20^{\circ}=\mathrm{k}\), then \(\frac{4 \mathrm{k}}{3}=\)AP EAMCET 2025 Medium
- In a class consisting of 40 boys and 30 girls. \(30 \%\) of the boys and \(40 \%\) of the girls are good at Mathematics. If a student selected at random from that class is found to be a girl, then the probability that she is not good at Mathematics isAP EAMCET 2024 Medium
- It is given that in a random experiment events A and B are such that \(\mathrm{P}(\mathrm{A})=\frac{1}{4}, P(A \mid B)=\frac{1}{2}\) and \(P(B \mid A)=\frac{2}{3}\) then \(P(B)=\)
\(\frac{1}{6}\)AP EAMCET 2024 Easy - If \(\int\left(\frac{4 e^x+6 e^{-x}}{9 e^x-4 e^{-x}}\right) d x=A x+B \log \left|\left(9 e^{2 x}-4\right)\right|+C\), then \((\mathrm{A}, \mathrm{B})=\)AP EAMCET 2023 Medium
More PYQs from AP EAMCET
- If the point of intersection of the tangents drawn at the points where the line \(5 x+y+1=0\) cuts the circle \(x^2+y^2-2 x-6 y-8=0\) is \((\underline{a, b})\), then \(5 a+b=\)AP EAMCET 2017 Medium
- The area of the region (in sq.units) bounded by the curves \(x^2+y^2=16\) and \(\mathrm{y}^2=6 \mathrm{x}\) isAP EAMCET 2025 Medium
- The oxidation state of \(\mathrm{Xe}\) in \(\mathrm{XeO}_3\) and the bond angle in it respectively are:AP EAMCET 2003 Easy
- The maximum distance between the transmitting and receiving TV towers is \(65 \mathrm{~km}\). If the ratio of the heights of the TV transmitting tower to receiving tower is \(36: 49\), the heights of the transmitting and receiving towers respectively are (radius of earth \(=6400 \mathrm{~km}\))AP EAMCET 2018 Medium
- If the charge on the capacitor is \(1 \mathrm{mC}\) in the given circuit,
then \(\frac{R_1 R_2}{R_3}=\ldots \ldots \ldots . . . . \Omega\).AP EAMCET 2017 Medium - If \(\mathrm{P}=(\overline{\mathrm{a}} \times \overline{\mathrm{i}})^2+(\overline{\mathrm{a}} \times \overline{\mathrm{j}})^2+(\overline{\mathrm{a}} \times \overline{\mathrm{k}})^2\) and \(\mathrm{Q}=(\overline{\mathrm{a}} \cdot \overline{\mathrm{i}})^2+(\overline{\mathrm{a}} \cdot \overline{\mathrm{j}})^2+(\overline{\mathrm{a}} \cdot \overline{\mathrm{k}})^2\), thenAP EAMCET 2025 Medium