Solve each of the following initial value problems: `(dy)/(dx)+(2x)/(x^2+1)y=1/((x^2+1)^2),y(0)=0` (ii) `(x^2+1)y -2x y=(x^4+2x^2+1)cosx ,y(0)=0`

Solve each of the following initial value problems: (dy)/(dx)+(2x)/(x^2+1)y=1/((x^2+1)^2),y(0)=0 (ii) (x^2+1)(dy)/(dx) -2x y=(x^4+2x^2+1)cosx ,y(0)=0

Solve each of the following initial value problems: (dy)/(dx)+(2x)/(x^(2)+1)y=(1)/((x^(2)+1)^(2)),y(0)=0( ii) (x^(2)+1)y'-2xy=(x^(4)+2x^(2)+1)cos x,y(0)=0

Solve each of the following initial value problem: (dy)/(dx)+2y=e^(-2x)sin x,y(1)=0

Solve the following initial value problem: (dy)/(dx)=2e^(2x)y^(2),y(0)=1

Solve each of the following initial value problem: 2x^2(dy)/(dx)-2x y+y^2=0,\ y(e)=e

Solve the following initial value problem: (dy)/(dx)=y sin2x,y(0)=1

Solve the following initial value problem: (dy)/(dx)=y sin2x,y(0)=1

Solve each of the following initial value problem: x(dy)/(dx)-y+x sin((y)/(x))=0,y(2)=x

Solve each of the following initial value problem: (dy)/(dx)+y tan x=2x+x^(2)tan x,y(0)=1

Solve the following initial value problems : x(dy)/(dx)+2y=x^(2),y(1)=1/4