TS EAMCET · Maths · Differential Equations
An integrating factor of the differential equation \(\left(1-x^2\right) \frac{d y}{d x}+x y=\frac{x^4}{\left(1+x^5\right)}\left(\sqrt{1-x^2}\right)^3\) is
- A \(\sqrt{1-x^2}\)
- B \(\frac{x}{\sqrt{1-x^2}}\)
- C \(\frac{x^2}{\sqrt{1-x^2}}\)
- D \(\frac{1}{\sqrt{1-x^2}}\)
Answer & Solution
Correct Answer
(D) \(\frac{1}{\sqrt{1-x^2}}\)
Step-by-step Solution
Detailed explanation
Given differential equation can be rewritten as \(\begin{aligned} & \frac{d y}{d x}+\frac{x y}{1-x^2}=\frac{x^4\left(\sqrt{1-x^2}\right)^3}{\left(1+x^5\right)\left(1-x^2\right)} \\ & \frac{d y}{d x}+\frac{x y}{1-x^2}=\frac{x^4 \sqrt{1-x^2}}{\left(1+x^5\right)}\end{aligned}\) On…
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 \(k=\frac{a+b}{a b}\) is a non-zero constant then the point which lies on the straight line \(\frac{x}{a}+\frac{y}{b}=1\) isTS EAMCET 2023 Easy
- The curve \(y=x^3-2 x^2+3 x-4\) intersects the horizontal line \(y=-2\) at the point \(P(h, k)\). If the tangent drawn to this curve at P meets the \(X\)-axis at \(\left(x_1, y_1\right)\), then \(x_1=\)TS EAMCET 2024 Medium
- is a complex number such that and . The area of the region formed by locus of is (in sq. units)TS EAMCET 2018 Medium
- If \(R: r_1: r=5: 12: 2\), then \(r+r_3+r_2-r_1=\)TS EAMCET 2020 Hard
- Let ' \(a\) ' be a positive real number. If a real valued function
\(f(x)= \begin{cases}\frac{6^x-3^x-2^x+1}{1-\cos \left(\frac{x}{a}\right)} & \text { if } x \neq 0 \\ \log 3 \log 4 & \text { if } x=0\end{cases}\)
is continuous at \(x=0\), then \(a=\)TS EAMCET 2025 Medium - If a line having slope 2 is a tangent to the curve \(y=x^4-6 x^3+13 x^2-12 x+5\) at points \(P\left(x_1, y_1\right)\) and \(Q\) \(\left(\mathrm{x}_2, \mathrm{y}_2\right), \mathrm{x}_1, \mathrm{x}_2 \in \mathrm{N}\) then \(\mathrm{x}_1 \mathrm{x}_2-\mathrm{y}_1 \mathrm{y}_2=\)TS EAMCET 2023 Easy
More PYQs from TS EAMCET
- In a \(500 \mathrm{~mL}\) flask, the degree of dissociation of \(\mathrm{PCl}_5\) at equilibrium is \(40 \%\) and the initial amount is 5 moles. The value of equilibrium constant in \(\mathrm{mol} \mathrm{L}^{-1}\) for the decomposition of \(\mathrm{PCl}_5\) isTS EAMCET 2008 Medium
- Identify the incorrect statement regarding acetic acid.TS EAMCET 2021 Easy
- The radius of a sphere is changing. At an instant of time the rate of change in its volume and its surface area are equal. Then the value of radius at that instant is?TS EAMCET 2020 Easy
- If a function \(f:(-1,1) \rightarrow B(\subseteq R)\) is defined as \(f(x)=x+x^2+x^3+\ldots \infty\), then in order to have the inverse function of \(f, B\) is equal toTS EAMCET 2021 Easy
- 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 isTS EAMCET 2012 Easy
- If the perpendicular distance from the focus of an ellipse \(\frac{x^2}{9}+\frac{y^2}{b^2}=1(b < 3)\) to its corresponding directrix is \(\frac{4}{\sqrt{5}}\), then the slope of the tangent to this ellipse drawn at \(\left(\frac{3}{\sqrt{2}}, \frac{b}{\sqrt{2}}\right)\) isTS EAMCET 2025 Medium