What is a particular solution to the differential equation #dy/dx=-x/y# with #y(4)=3#?

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Answer 1 · 2016-07-18T15:10:55

#y = pm sqrt(25 - x^2)#

equation is separable as follows

#y dy/dx = -x#

#int \ y dy/dx \ dx =int\ -x \ dx#

#int \ y \ dy = - int\ x \ dx#

#y^2/2 = - (x^2/2 - C)#

#y^2/2 = C - x^2/2#

#y^2 = C - x^2#

applying the IV

#9 = C - 4^2, implies C = 19#

#y^2 = 25 - x^2#

#y = pm sqrt(25 - x^2)#