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

Solve: 1. (x+1)(dy)/(dx)=2x y 2. cosx(1+cosy)dx-s in y(1+sinx)dy=0

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

Solve the following differential equations. 2(x-3y+1)(dy)/(dx)=(4x-2y+1)

Find the order and degree of the following differential equations. i) (dy)/(dx)+y=1/((dy)/(dx)) , ii) e^(e^(3)y)/(dx^(3))-x(d^(2)y)/(dx^(2))+y=0 , iii) sin^(-1)(dy)/(dx)=x+y , iv) log_(e)(dy)/(dx)=ax+by v) y(d^(2)y)/(dx^(2))+x((dy)/(dx))^(2)-4y(dy)/(dx)=0

If y = sqrt(1+sqrt(1+x^(4))) , prove that y * (y^(2) - 1)(dy)/(dx) = x^(3) .

Solve: (i) sin^(-1)((dy)/(dx))=x+y (ii) (dy)/(dx)=cos(x+y) (iii) (dy)/(dx)=(4x+y+1)^2

Find dy/dx if y= 2x+3y

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

Find dy/dx if 3= 2x-3y

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