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

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

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

Find (dy)/(dx) if,y=((x^(2)-1)^(3)(2x-1))/(sqrt((x-3)(4x-1)))

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

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

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

If y_(1)(x) and y_(2)(x) are two solutions of (dy)/(dx)+f(x)y=r(x), then y_(1)(x)+y_(2)(x) is solution of : (A) (dy)/(dx)+f(x)y=0 (B) (dy)/(dx)+2f(x)y=r(x)(C)(dy)/(dx)+f(x)y=2r(x)(D)(dy)/(dx)+2f(x)y=2r(x)

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

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

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