AP EAMCET · Maths · Differential Equations
The general solution of the differential equation \(\frac{d y}{d x}=\frac{2 x y-4 x+y-2}{2 x y+x-4 y-2}\) is
- A \(5(y-x)+2 \log \left(\frac{y-2}{x-2}\right)=c\)
- B \(2(y-x)-5 \log \left(\frac{y-2}{x-2}\right)=c\)
- C \(2(y-x)+5 \log \left(\frac{y-2}{x-2}\right)=c\)
- D \(5(y-x)-2 \log \left(\frac{y-2}{x-2}\right)=c\)
Answer & Solution
Correct Answer
(C) \(2(y-x)+5 \log \left(\frac{y-2}{x-2}\right)=c\)
Step-by-step Solution
Detailed explanation
\(\frac{d y}{d x}=\frac{(2x+1)(y-2)}{(x-2)(2y+1)}\) \(\int \frac{2y+1}{y-2} dy = \int \frac{2x+1}{x-2} dx\) \(\int \left(2 + \frac{5}{y-2}\right) dy = \int \left(2 + \frac{5}{x-2}\right) dx\) \(2y + 5 \log|y-2| = 2x + 5 \log|x-2| + c'\)…
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
- For all \(\mathrm{n} \in \mathrm{N}\), if \(1^3+2^3+3^3+\ldots. .+\mathrm{n}^3>\mathrm{x}\), then a value of x among the following isAP EAMCET 2025 Easy
- If two sides of a triangle are given by \(3 x^2-5 x y+2 y^2=0\) and its orthocentre is \((2,1)\), then the equation of the third side of the triangle isAP EAMCET 2018 Medium
- If each of the observations \(x_1, x_2, \ldots, x_n\) is increased or decreased by \(k\), where \(k\) is a positive number, then the variance of the daAP EAMCET 2023 Easy
- If \(f: R \rightarrow C\) is defined by \(f(x)=e^{2 i x}\) for \(x \in R\), then \(f\) is (where \(C\) denotes the set of all complex numbers)AP EAMCET 2008 Medium
- The equation of the common tangent to the parabolas \(y^2=32 x\) and \(x^2=256 y\) isAP EAMCET 2017 Medium
- The equation of the circle circumscribing the triangle formed by the straight lines \(x+y=6\). \(2 x+y=4\) and \(x+2 y=5\) is given byAP EAMCET 2020 Medium
More PYQs from AP EAMCET
- A projectile is thrown in the upward direction making an angle of \(60^{\circ}\) with the horizontal with a velocity of \(140 \mathrm{~ms}^{-1}\). Then the time after which its velocity makes an angle \(45^{\circ}\) with the horizontal is (Acceleration due to gravity, \(g=10 \mathrm{~ms}^{-2}\) )AP EAMCET 2019 Medium
- If and thenAP EAMCET 2019 Medium
- The pair of oxides, which can be leached out, when powdered bauxite containing certain impurities is digested with concentrated solution of \(\mathrm{NaOH}\) at \(473-523 \mathrm{~K}\) temperature and \(35-36\) bar pressure areAP EAMCET 2018 Medium
- The ratio between RMS velocities of \(\mathrm{H}_2\) at \(50 \mathrm{~K}\) and \(\mathrm{O}_2\) at \(800 \mathrm{~K}\) isAP EAMCET 2019 Easy
- If the sum of the roots of the quadratic equations is 1 and sum of the squares of the roots is 13 , then find that equation.AP EAMCET 2020 Easy
- \([\mathrm{x}]\) represents the greatest integer function.
If \(\lim _{x \rightarrow 0^{+}} \frac{\cos [x]-\cos (k x-[x])}{x^2}=5\) then \(k=\)AP EAMCET 2025 Hard