AP EAMCET · Maths · Differential Equations
The solution of \(\left(1+x^2\right) \frac{d y}{d x}+2 x y-4 x^2=0\) is :
- A \(3 x\left(1+y^2\right)=4 y^3+c\)
- B \(3 y\left(1+x^2\right)=4 x^3+c\)
- C \(3 x\left(1-y^2\right)=4 y^3+c\)
- D \(3 y\left(1+y^2\right)=4 x^3+c\)
Answer & Solution
Correct Answer
(B) \(3 y\left(1+x^2\right)=4 x^3+c\)
Step-by-step Solution
Detailed explanation
\(\left(1+x^2\right) \frac{d y}{d x}+2 x y-4 x^2=0\) \(\Rightarrow \quad \frac{d y}{d x}+\left(\frac{2 x}{1+x^2}\right) y=\frac{4 x^2}{1+x^2}\) On comparing with \(\frac{d y}{d x}+P y=Q\), we get \(P=\frac{2 x}{1+x^2}, Q=\frac{4 x^2}{1+x^2}\) I.F.…
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
- In \(\triangle A B C, \sqrt{\frac{r r_2}{r_3 r_1}}=\)AP EAMCET 2025 Medium
- The number of solutions of the following system of linear homogeneous equations \(x-y+z=0, x+2 y-z=0\) and \(2 x+y+3 z=0\) isAP EAMCET 2021 Medium
- Let be three non zero complex numbers such that . if the determinant , thenAP EAMCET 2021 Easy
- If \(\mathbf{a}+\mathbf{b}+\mathbf{c}=0\) and \(|\mathbf{a}|=3,|\mathbf{b}|=5,|\mathbf{c}|=7\), then the angle between \(\mathbf{a}\) and \(\mathbf{b}\) is ........AP EAMCET 2020 Easy
- A point moves in the \(x y\)-plane such that the sum of its distance from two mutually perpendicular lines is always equal to 5 units. The area (in sq units) enclosed by the locus of the point, isAP EAMCET 2012 Hard
- If \(x=a\left\{\cos \theta+\log \tan \left(\frac{\theta}{2}\right)\right\}\) and \(y=a \sin \theta\), then \(\frac{d y}{d x}\) is equal toAP EAMCET 2008 Medium
More PYQs from AP EAMCET
- The depression in freezing point of solution of molality \(0.01 \mathrm{~mol} \mathrm{~kg}^{-1}\) is highest with respect to which of the solvent? (Whose \(K_f\) is given in brackets)AP EAMCET 2022 Medium
- The distance between the directrices of the ellipse \(\frac{x^2}{36}+\frac{y^2}{20}=1\) isAP EAMCET 2022 Easy
- If the line passing through the points \((5,1, a)\) and \((3, b, 1)\) crosses the YZ plane at the point \(\left(0, \frac{17}{2}, \frac{-18}{2}\right)\), then \(a+b=\)AP EAMCET 2023 Medium
- In the following logic circuit, the values of \(\mathrm{Y}_1, \mathrm{Y}_2\) and \(\mathrm{Y}_3\) are respectively
AP EAMCET 2017 Easy - The catalyst and promoter respectively used in the Haber's process of industrial synthesis of ammonia areAP EAMCET 2012 Easy
- The surface tension and vapour pressure of a liquid at \(25^{\circ} \mathrm{C}\) are \(8 \times 10^{-2} \mathrm{Nm}^{-1}\) and \(2.5 \times 10^3 \mathrm{~Pa}\) respectively. The radius of the smallest spherical water droplet which can from without evaporating at \(25^{\circ} \mathrm{C}\) isAP EAMCET 2022 Hard