Q. 175.0( 1 Vote )

Solve the followi

Answer :

We have given

We can write it as,



Now, The equation is in the form of a linear differential equation as



When we compare the equation with the linear equation , we get





Let x2 - 1 = t then 2xdx = dt





When substituting the value of t , we get


I.F = x2 - 1 + C


Now, The general solution for a linear equation is






Hence, This the required solution of given differential equation.


OR


Re - writing the equation as





Now separating variable x on one side and variable y on another side, we have



Multiplying and dividing the numerator of LHS by x



Assuming 1+y2 = t2 and 1+x2 = v2


Differentiating we get,


ydy = tdt


xdx = vdv


Substituting these values in above differential equation



Integrating both sides



Adding 1 and subtracting 1 to the numerator of RHS



We know that,



Therefore,



Substituting t and v in above equation



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