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

Question

5167 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-03-13T02:40:03

$y^2 = 25 - x^2$

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 $y(4)=3$ then:

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

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 $5$ centred on the origin.

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