Q. 215.0( 1 Vote )

Solve the differe

Answer :

Given equation:


On-rearranging the term, we get,





Now, this is a homogenous differential equation of order 1.


Let y = vx and


Therefore,





Integrating both sides, we get,



Now, we know that,


and


Therefore,




Putting the value of y, we get,



At x = 1, y = 0,



C = 1


Hence,




OR


Given Equation:


Dividing the whole equation by (1 + x2), we get,



Now, this is a linear equation of the form,



We know that the solution of this equation is given by,



Where


Therefore, for a given equation,



Let 1 + x2 = t


Differentiating both sides, we get,


2x dx = dt


Therefore,




The solution of the equation:





At x = 0, y = 0


Therefore,


0(1 + 0) = 0 + c
c = 0

Hence,

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