InterviewSolution
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InterviewSolution
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हल कीजिए- `(1+x^(2))dy+2 xydx=cot dx.` |
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Answer» दिया गया अवकल समीकरण है- `(1+x^(2))dt+2xydx=cot xdx` `implies(1+ x^(2))(dy)/(dx) +2xy =cot ` `implies(dy)/(dx) +(2x)/(1+x^(2))y=(cot x)/(1+c^(2))" "...(1)` यहाँ `P=(2x)/(1+x^(2)),Q=(cot x)/(1+x^(2))` ` therefore I . F. =e ^(intPdx)=e ^(int (2x)/(1+x^(2))dt)` `=e^(int (dt)/(t)), ["माना"1+x^(2)=timplies 2 xdx=dt]` `=e^(log|t|)=e^(log |1+x^(2)|)=1+x^(2)` यही अभीष्ट व्यापक हल है- `yxx (I.F.) =int Q xx (I.F.)dt +C` `impliesy(1+x^(2))=int(cot x)/(1+x^(2))xx(1+x^(2)) dx+C` `impliesy(1+x^(2))=intcot x dx +C` `impliesy (1+x^(2))=log |sin x| +C` `implies y=(log |sin x|)/(1+x^(2))+(C)/(1+x^(2)).` |
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