InterviewSolution
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InterviewSolution
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हल कीजिए `(x+y) ^(2)(dy)/(dx) =a^(2)` |
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Answer» दिया गया अवकल समीकरण है. `(x+y) ^(2)(dy)/(dx)=a^(2)` `implies(dy)/(dx)= (a^(2))/((a+y)^(2))" "...(1)` माना `x+y =v" "...(2)` x के सापेक्ष अवकलन करने पर, `1+(dy)/(dx)=(dv)/(dx)` `implies(dy)/(dx) =(dv)/(dx)-1" "...(3)` समी (1 ) (2 ) और (3 ) से, `(dv)/(dx)-1(a^(2))/(v^(2))` `implies(dv)/(dx)=(a^(2))/(v^(2))+1` `implies (dv)/(dx) =(a^(2)+v^(2))/(v^(2))` `implies (v^(2))/(a^(2)+v^(2)) dv =dx,` (चरो के पृथक्करण से) समाकलन करने पर, `int (v^(2))/(a^(2)+ v^(2))dv=int dx ` `impliesint ((a^(2) +v^(2))-a^(2))/(a^(2)+v^(2))dv = intdx` `implies int (1-(a^(2))/(a^(2)+ v^(2)))dv = x+C` `implies int 1 dv -a^(2) int (1)/(a^(2)+v^(2))dv= x+C` `impliesv -a^(2) xx1/a tan ^(-1) ((v)/(a))=x+C` `implies v- tan^(-1) ((v)/(a))=x+C` `implies y-a tan ^(-1) ((x+y)/(a))=C.` |
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