InterviewSolution
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InterviewSolution
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`x dy-y dx=sqrt(x^(2)+y^(2))dx` |
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Answer» `x dy-y dx=sqrt(x^(2)+y^(2))dx` `implies x dy=(y+sqrt(x^(2)+y^(2)))dx` `implies (dy)/(dx)=(y+sqrt(x^(2)+y^(2)))/(x)" ....(1)"` माना y = vx `implies (dy)/(dx)=v+x(dv)/(dx)` समीकरण (1) से, `v+x(dv)/(dx)=(vx+sqrt(x^(2)+v^(2)x^(2)))/(x)` `=v+sqrt(v^(2)+1)` `implies x(dv)/(dx)=sqrt(v^(2)+1)` `implies (dv)/(sqrt(v^(2)+1))=(dx)/(x)` `implies int(1)/(sqrt(v^(2)+1))dv=int(dx)/(x)` `implies log(v+sqrt(v^(2)+1))=logx+logc=log(cx)` `implies v+sqrt(v^(2)+1)=cx` `implies (y)/(x)+sqrt((y^(2))/(x^(2))+1)=cx` `implies y+sqrt(y^(2)+x^(2))=cx^(2)` |
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