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

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

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

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

The solution of (dy)/(dx) + (3)/(x) y = (1)/(x^(2)) , at y=2, x=1

For each of the following differential equations verify that the accompanying functions a solution. (i) x(dy)/(dx)=y => y=a x (ii) x+y(dy)/(dx)=0 => y=+-sqrt(a^2-x^2) (iii) x(dy)/(dx)y+y^2 => y=a/(x+a) (iv) x^3(d^2y)/(dx^2)=1 => y=a x+b+1/(2x) (v) y=((dy)/(dx))^2 => y=1/4(x+-a)^2

(dy)/(dx)+(3y)/(x)=(1)/(x^(2)) , given that y = 2 when x = 1.

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

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!)+... i s