# Chapter 10 - Introduction to Differential Equations - Chapter Review Exercises - Page 525: 4

$$y= (2\ln x- x^2+c)^{1/2}.$$

#### Work Step by Step

By separation of variables, we have $$ydy=(\frac{1}{x}-x)dx$$ then by integration, we get $$\frac{1}{2}y^2=\ln x-\frac{1}{2}x^2+c .$$ So the general solution is given by $$y= (2\ln x- x^2+c)^{1/2}.$$

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