COMEDK · Maths · 32. Differential Equations
\(\text { Integrating factor of the differential equation } \dfrac{d y}{d x}+y=\dfrac{x^3+y}{x} \text { is }\)
- A \(x e^x\)
- B \(\dfrac{e^x}{x}\)
- C \(\dfrac{x}{e^x}\)
- D \(e^x\)
Answer & Solution
Correct Answer
(B) \(\dfrac{e^x}{x}\)
Step-by-step Solution
Detailed explanation
The given differential equation is \(\dfrac{dy}{dx} + y = \dfrac{x^3 + y}{x}\). Rearranging the terms to the standard form \(\dfrac{dy}{dx} + P(x)y = Q(x)\), we have: \(\dfrac{dy}{dx} + y = x^2 + \dfrac{y}{x}\) \(\dfrac{dy}{dx} + y - \dfrac{y}{x} = x^2\)…
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