Comprehension

Direction : Consider the following for the items that follow :

Let ydx + (x - y3)dy = 0 be a differential equation.  

What is the solution of the differential equation? 

This question was previously asked in
NDA-II 2024 (Maths) Official Paper (Held On: 01 Sept, 2024)
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  1. y4 + 2x = c
  2. y4 + 3x = c
  3. 2xy4 + x = c
  4. 4xy - y4 = c

Answer (Detailed Solution Below)

Option 4 : 4xy - y4 = c
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Detailed Solution

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Explanation:

ydx + (x – y3 )dy = 0

\(y\frac{dy}{dx}+ x = y^3\)

\(\frac{dx}{dy} + x \frac{1}{y} - y^2\)  (linear differential equation)

L.E = \(e^{\int\frac{1}{y}dy}\) = y

x(L.F) = \(\int(LE)y^2dy\)

xy = \(\int y^3dy\)

⇒ 4xy – y4 = c

∴ Option (d) is correct

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