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AP EAMCET · Maths · Differential Equations

The integrating factor of the linear directional equation \(\frac{d y}{d x}+P(x) y=Q(x)\) is a solution of the differential equation

  1. A \(\frac{d y}{d x}-P(x) y=0\)
  2. B \(\frac{d y}{d x}+P(x) y=0\)
  3. C \(\frac{d y}{d x}-\frac{y}{x}=P(x)\)
  4. D \(\frac{d y}{d x}+\frac{x}{y}=P(x)\)
Verified Solution

Answer & Solution

Correct Answer

(A) \(\frac{d y}{d x}-P(x) y=0\)

Step-by-step Solution

Detailed explanation

\(\frac{d y}{d x}+P(x) y=Q(x)\) \(\begin{aligned} & \text { Integrating }=e^{\int P(x) d x} \\ & \text { Factor }\end{aligned}\) (A) If \(y=e^{\int p(x) d x}\) checking: \(\frac{d y}{d x}-P(x) y=0\) \(\frac{d y}{d x}=e^{\int {p}(x) d x}\) \(P(x)=y P(x)\)…