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  • What is the eq. of the curve passing through the point (?/2,1) and having slope sinx/x^2 - 2y/x at each point (x,y) with x?0.

What is the eq. of the curve passing through the point (?/2,1) and having slope sinx/x^2 - 2y/x at each point (x,y) with x?0.

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We;need;to;use;the;solution;methods;of;the;first;order;differential\* equations;for;this.; This;particular;case,;is;easier;and;solvable;also \*this;way.\* slope=fracmathrmd ymathrmd x=fracsin xx^2 - frac2yx\* Rightarrow x^2fracmathrmd ymathrmd x+(2x)y=sin x\* LHS;is;derivative;x^2y;w.r.t.;x\* Rightarrow x^2fracmathrmd ymathrmd x+(2x)y=fracmathrmd (x^2y)mathrmd x=sin x\* Now,;integrate;both;side\* x^2y=int sin x ;dx\* Rightarrow x^2y=-cos x+c\* y=frac-cos x+cx^2\* ecause (fracpi2, 1);lies;on;the;curve\* herefore 1=fracc-0fracpi ^24\* c=frac4pi ^2\* The;required;curve;is;y=fracfrac4pi ^2-cos xx^2,;x eq 0

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Deependra Verma

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