AP 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…
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