Question
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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?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFव्याख्या:
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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