If `y=1+c_1/(x-c_1)+(c_2x)/((x-c_1)(x-c_2))+(c_3 x^2)/((x-c_1)(x-c_2)(x-c_3))` show that `dy/dx=(y/x)[c_1/(c_1-x)+c_2/(c_2-x)+c_3/(c_3-x)]`

If y=(ax^(2))/((x-a)(x-b)(x-c))+(bx)/((x-b)(x-c))+(c)/(x-c)+1 find (dy)/(dx)

The solution of ((dy)/(dx))^(2)+(2x+y)(dy)/(dx)+2xy=0, is (i) (y+x^(2)-c_(1))(x+log y+y^(2)+c_(2))( (ii) (y+x^(2)-c_(1))(x-log y-c_(2))( iii) (y+x^(2)-c_(1))(x+log y-c_(2))( iv) (y+x^(2)-c_(1))(3x+log y-c_(2))

Tan^(-1)((c_(1)x-y)/(c_(1)y+x))+Tan^(-1)((c_(2)-c_(1))/(1+c_(2)c_(1)))+Tan^(-1)((c_(3)-c_(2))/(1+c_(3)c_(2)))+…+Tan^(-1)(1/c_(n))=

"Tan"^(-1)(c_(1)x-y)/(c_(1)y+x)+"Tan"^(-1)(c_(2)-c_(1))/(1+c_(2)c_(1))+"Tan"^(-1)(c_(3)-c_(2))/(1+c_(3)c_(2))+..."Tan"^(-1)1/c_(n)=

If (x)/((1+x^(2))(3-2x))=(A)/(3-2x)+(Bx+C)/(1+x^(2)) then C=

If (x)/((1+x^(2))(3-2x))=(A)/(3-2x)+(Bx+C)/(1+x^(2)) then C=