# Chapter 1 - First-Order Differential Equations - 1.3 The Geometry of First-Order Differential Equations - Problems: 9

See below.

#### Work Step by Step

Differentiate the equation in respect to $x$. $$x^2+y^2=c$$ $$2x+2y \times y'=0$$ Solve for $y'$. $$y \times y'=-x$$ $$y'=-\frac{x}{y}$$ This expression matches the given differential equation $y'=-x/y$ exactly, therefore, the equation is a solution.

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