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

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

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

Find IF of x(dy)/(dx)+y=x^(3) .

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

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

Integrating factor of : (dy)/(dx)+(y)/(x)=x^(3)-3x is

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

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

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