InterviewSolution
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InterviewSolution
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अवकल समीकरण को हल कीजिए- `x log x (dy)/(dx) +y =2/x log x.` |
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Answer» दिया गया अवकल समीकरण है- `x log x (dy)/(dx) +y=2/x log x` `implies(dy)/(dx) +((1)/(x log x)) y=(2 log x)/(x^(2)log x)` `implies(dy)/(dx)+((1)/(x log x))y= (2)/(x^(2))" "...(1)` जो कि y रैखिक अवकल समीकरण है. समी (1 ) की तुलना मानक रूप `(dy)/(dx) +Py =Q` से करने पर, `P =(1)/(xlog x ) ` और `Q =(2)/(x^(2))` `thereforeI .F. =e^(int Pdx)=e ^(int (1)/(x log x))` `e ^(int (1)/(t)dt) , [" माना" log x =1 implies(1)/(x)dx =dt ]` `=e ^(log |t|)=|t|=log x` अतः अभीष्ट हल है- `yxx (I.F.) =int Q . (I. F.) dx+C` `impliesy log x = int (2)/(underset(II)(x^(2)))underset(I)(log ) x dx +C` `implies y log x = log x int (2)/(x^(2)) dx` `-int {(d)/(dx)(log x). int (2)/(x^(2))dx}dx+C` `impliesy log x = log x (-(2)/(x))-int ((1)/(pi)xx(-2)/(x))dx+C` `impliesy log x =- (2)/(x) log x+ int (2)/(x^(2))dx+C` `implies y log x =-(2)/(x) log x- (2)/(x)+C.` |
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