InterviewSolution
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InterviewSolution
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`{xcos((y)/(x))+y sin((y)/(x))}y dx={ysin((y)/(x))-xcos((y)/(x))}x dy` |
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Answer» `(xcos.(y)/(x)+y sin.(y)/(x))y dx` `=(ysin.(y)/(x)-xcos.(y)/(x))x dy` `implies (dy)/(dx)=(y(cos.(y)/(x)+ysin.(y)/(x)))/(x(ysin.(y)/(x)-xcos.(y)/(x)))` `implies v+x(dv)/(dx)=(vx(xcosv+vxsinv))/(x(vxsinv-xcosv))` `=(v(cosv+vsinv))/(vsinv-cosv)` माना `y = vx implies (dy)/(dx)=v+x(dv)/(dx)` `implies x(dv)/(dx)=(vcosv+v^(2)sinv)/(vsinv-cosv)-v` `=(vcosv+v^(2)sinv-v^(2)sinv+vcosv)/(vsinv-cosv)` `impliesx(dv)/(dx)=(2v cosv)/(vsinv-cosv)` `implies (vsinv-cosv)/(vcosv)dv=2(dx)/(x)` `implies int(tanv-(1)/(v))dv=2int(dx)/(x)+logc` `implies logsecv-logv=2logx+logc` `implies log((secv)/(v))=log(cx^(2))` `implies (secv)/(v)=cx^(2)` `implies secv=cx^(2)v` `implies sec.(y)/(x)=cxy` |
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