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" 3."quad (dy)/(dx)+(y)/(x)=x^(2)...

" 3."quad (dy)/(dx)+(y)/(x)=x^(2)

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(dy)/(dx)+(1)/(2x)y=(x)/(y^(3))

The integrating factor of the differential equation 3(dy)/(dx)+(3y)/(x)=2x^(4)y^(4) is -

(dy)/(dx)=(2x+3y)/(3x+2y)

(dy)/(dx)=(2x-3y)/(3x-2y)

(dy)/(dx)=(x+y)/(2(x+y)+3)

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

dy/dx =(y)/(2y^3+x)

(dy)/(dx)=(x+y+1)/(2x+2y+3)

(dy)/(dx)=(x+y+1)/(2x+2y+3)