Q. 155.0( 2 Votes )

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

Answer :

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




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