# How do you solve this differential equation #dy/dx=(-x)/y# when #y=3# and #x=4# ?

##### 1 Answer

Mar 13, 2018

# y^2 = 25 - x^2 #

#### Explanation:

We have:

# dy/dx=(-x)/y# with#y=3# when#x=4#

This is a separable ODE, so we can write:

# y \ dy/dx = -x #

Then we can *"separate the variables"* :

# int \ y \ dy = - \ int \ x \ dx #

Then we can readily integrate to get:

# 1/2y^2 = - 1/2x^2 + C #

Given the initial condition

# 1/2 * 9 = - 1/2 * 16 + C => C = 25/2 #

So the Particular Solution is:

# 1/2y^2 = - 1/2x^2 + 25/2 #

# :. y^2 = 25 - x^2 #

Which we note is a circle of radius