Find the equation of a curve passing through origin and satisfying the differential equation

given: and (0,0) is a solution to the curve

To find: equation of curve satisfying this differential equation

Re-writing the equation as

Comparing it with

Calculating integrating factor

Calculating

Assume 1+x²=t

2x dx=dt

Formula:

Substituting t=1+x²

IF=1+x²

Therefore, the solution of the differential equation is given by

Formula:

Satisfying (0,0) in the curve equation to find c

0=0+c

c=0

therefore, the equation of curve is