Comprehension

निर्देश : निम्नलिखित प्रश्नों के लिए निम्नलिखित पर विचार करें:

माना ydx + (x - y3)dy = 0 एक अवकल समीकरण है।

अवकल समीकरण का हल क्या है?

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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NDA 01/2025: English Subject Test
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Detailed Solution

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व्याख्या:

ydx + (x - y3 )dy = 0

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

\(\frac{dx}{dy} + x \frac{1}{y} = y^2\) (रैखिक अवकल समीकरण)

समाकलन गुणक (L.E) = \(e^{\int\frac{1}{y}dy}\) = y

x(समाकलन गुणक) = \(\int(समाकलन गुणक)y^2dy\)

xy = \(\int y^3dy\)

⇒ 4xy - y4 = c

∴ विकल्प (d) सही है

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