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

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

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The solution of the differential equation x(x^2+1)((dy)/(dx))=y(1-x^2)+x^3logx is

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

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

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

x dy/dx+y=y^2 logx

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

The solution of 3x(1-x^2)y^2dy / dx+(2x^2-1)y^3=a x^3 is

x(dy)/(dx)=y(logy-logx+1)

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

If y=sin(x^x) , prove that (dy)/(dx)=cos(x^x) .x^x(1+logx)

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