# Chapter 1 - First-Order Differential Equations - 1.2 Basic Ideas and Terminology - Problems: 11

See below.

#### Work Step by Step

Take the derivative of the function. $$y(x)=c_1x^{1/2}$$ $$y'(x)=\frac{1}{2}c_1x^{-1/2}$$ Substituting this function into the differential equation yields $$y'=\frac{y}{2x}$$ $$\frac{1}{2}c_1x^{-1/2}=\frac{c_1x^{1/2}}{2x}$$ $$\frac{1}{2}c_1x^{-1/2}=\frac{1}{2}c_1x^{-1/2}$$ Since the equation is true, the solution is valid and it is valid for all real numbers. The interval linked to this solution is $[0,\infty)$.

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