(x^(3)+x^(2)+x+1)(dy)/(dx)2x^(2)+x;y=14 pi x

x(dy)/(dx)+y=3x^(2)-2,x>0

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

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

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

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

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

For each of the following differential equations verify that the accompanying functions a solution. Differential Function (a) x(dy)/(dx)=y, y=a x (b) x+y(dy)/(dx)=0, y=+-sqrt(a^2-x^2) (c) x(dy)/(dx)y=y^2, y=a/(x+a) (d) x^3(d^2y)/(dx^2)=1, y=a x+b+1/(2x) (e) y=((dy)/(dx))^2, y=1/4(x+-a)^2

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

If y= (sin^(-1) x)^2 , then (1-x^2) (d^2 y)/(dx^2) - x (dy/dx) = ..........

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