Question
Download Solution PDF\(\rm {dy\over dx}+ \frac{y}{x} = 3\sin x\) का समाकल कारक खोजें।
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFअवधारणा:
पहले क्रम में रैखिक अवकल समीकरण;
\(\rm {dy\over dx}+Py=Q\) , जहां P और Q, x के फलन हैं
समाकल कारक (IF) = e∫ P dx
y × (IF) = ∫ Q(IF) dx
गणना:
\(\rm {dy\over dx}+ \frac{y}{x} = 3\sin x\)
IF = e∫ \(\frac{1}{x}\)dx
⇒ IF = eln x
⇒ IF = x
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