AP EAMCET · Maths · Differential Equations
Integrating factor of \(\left(x+2 y^3\right) \frac{d y}{d x}=y^2\) is
- A \(e^{\left(\frac{1}{y}\right)}\)
- B \(e^{-\left(\frac{1}{y}\right)}\)
- C \(y\)
- D \(\frac{-1}{y}\)
Answer & Solution
Correct Answer
(A) \(e^{\left(\frac{1}{y}\right)}\)
Step-by-step Solution
Detailed explanation
Given differential equation is \[ \begin{array}{rlrl} & & \left(x+2 y^3\right) \frac{d y}{d x}=y^2 \\ \Rightarrow & y^2 \frac{d x}{d y} & =x+2 y^3 \Rightarrow & \frac{d x}{d y}-\frac{x}{y^2}=2 y \\ \therefore & & I F & =e^{\int-\frac{1}{y^2} d y}=e^{\frac{1}{y}} \end{array} \]
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