`y' = 1/(xsqrt(4x^2-9))` Solve the differential equation.

Expert Answers

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Apply integral substitution: `x=3/2sec(u)`






Now use the identity:`sec^2(x)=1+tan^2(x)`



`y=inttan(u)/(3tan(u))du`  assuming `tan(u) >=0`


take the constant out,



Substitute back `u=arcsec((2x)/3)`

and add a constant C to the solution,


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