What is a solution to the differential equation \frac{dy}{dx}=-\frac{x}{y} with

Ryker Harvey

Ryker Harvey

Answered question

2022-04-19

What is a solution to the differential equation dydx=xy with the particular solution y(1)=2?

Answer & Explanation

xxkrnjangxxed9q

xxkrnjangxxed9q

Beginner2022-04-20Added 14 answers

ydy=-xdx
(12)y2=12x2+C
Because the form of C is arbitrary, we can write the above as our friend the circle:
x2+y2=C2
Forcing the initial condition:
12+(2)2=C2
C2=3
The equation becomes:
x2+y2=(3)2

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