Question
Download Solution PDF\(\rm\left( xy \frac {dy}{dx} -1 \right)= 0\) का सामान्य हल ज्ञात कीजिए।
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFसंकल्पना:
\(\rm \int \frac{1}{x}dx = \log x + c\)
\(\rm \int x^ndx = \frac{x^{n+1}}{n+1} + c\)
गणना:
दिया गया है:\(\rm\left( xy \frac {dy}{dx} -1 \right)= 0\)
\(\Rightarrow \rm xy \frac {dy}{dx} =1 \)
\(\Rightarrow \rm y \;dy=\frac {dx}{x} \)
दोनों पक्षों का समाकलन करने पर, हमें निम्न प्राप्त होता है
\(\rm \Rightarrow \frac{y^2}{2} = \log x + c\)
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