TS EAMCET · Maths · Differential Equations
An integrating factor of the equation \(\left(1+y+x^2 y\right) d x+\left(x+x^3\right) d y=0\) is
- A \(e^x\)
- B \(x^2\)
- C \(\frac{1}{x}\)
- D \(x\)
Answer & Solution
Correct Answer
(C) \(\frac{1}{x}\)
Step-by-step Solution
Detailed explanation
Given, differential equation is, \[ \begin{aligned} & d x\left(1+y+x^2 y\right)+\left(x+x^3\right) d y=0 \\ \Rightarrow \quad & \frac{d y}{d x}=-\left[\frac{1+y+x^2 y}{x+x^3}\right] \end{aligned} \]…
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