Question

The solution of the initial value problem dy/dx=-x/y, y(4)=3 is

Answer 1

Let's solve this equation using separate variables method.

Rearange terms:

$ydy = -xdx\\$

Integrate both sides of equation:

$\dfrac12 y^2 = -\dfrac12x^2+C\\$

Multiply by 2 and rearange terms again:

$x^2 + y^2 = C\\$

Obtain constant C from the initial conditions:

$4^2 + 3^2 = C\\ C = 5^2 = 25\\$

Thus, the final solution is:

$x^2 + y^2 = 25\\$

This is the equation of circle with radius 5.