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(6) dy/dx+xy=y^2e^(x^2/2)sinx...

(6) `dy/dx+xy=y^2e^(x^2/2)sinx`

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xy-dy/dx=y^3e^(-x^2)

dy/dx=(2xy)/(x^2-1-2y)

(a) dy/dx = (xy)/(x^2+y^2)

Solution of xy-(dy)/(dx)=y^(3)e^(-x^(2)) is

(dy)/(dx)=xy+2y+x+2

(dy)/(dx)=(x^(2)+y^(2))/(2xy)

xy (dy)/(dx) =x^(2) +2y^(2)

(dy)/(dx) = y tan x - 2 sinx