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Question:

Solution of the differential equation cosx dy = y(sinx - y)dx, 0 < x < π/2 is:

ysecx=tanx+c

tanx=(secx+c)y

ytanx=secx+c

secx=(tanx+c)y

Solution:

cosxdy=y(sinx−y)dx→dydx=ytanx−y2secx→1y2dydx+ytanx=−secxLet y=t→1y2dydx=dtdx→dtdx+t(tanx)=−secx.I.F=e∫tanxdx=secxSolution ist(I.F)=∫(I.F)(−secx)dx1ysecx=tanx+cHence, option 'A' is correct.