solve the differential equation 1/x dy/dx = - \sqrt xy

Question

solve the differential equation 1/x dy/dx = - \sqrt xy and give answer in terms of y(x)

Answer 1

This is separable if the equation is (1/x)dy/dx = -sqrt(xy)

dy/y^1/2 = -x^3/2dx)

Integrate both sides:

2y^1/2 = -(2/5)x^5/2 + C

y = (-(1/5)x^5/2 + C/2^')² = x⁵/25 - x^5/2C/5 + C²/4

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