Q. 2 - Calculus

Question

find an equation that gives y as an implicit function of x. Then draw the continuous curve that satisfies this differential equation and passes through the point (2, 0). 

$\frac{dy }{dx}=\frac{x}{y}$

Step-by-Step Solution

Answer

$x=y$

Step 1. Given information

$\frac{dy }{dx}=\frac{-x}{y}$

Step 2. Rearrange and integrate

$ydy=xdx$

$\int ydy=\int xdx$

$\frac{y^2}{2}=\frac{x^2}{2}$

$y^2=x^2$

$y=x$