Q. 18

Solve the following differential equations:


Answer :

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



Using identities:



and




Substituting t and v in above equation



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