What is a solution to the differential equation $xy' + 2y = 0$ ?

Question

29828 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-09-08T04:00:42

$y=C/x^2$

Write $y'$ as $dy/dx$ :

$xdy/dx+2y=0$

Try to separate the variables:

$xdy/dx=-2y$

$-1/(2y)dy=1/xdx$

Integrate both sides:

$-1/2int1/ydy=int1/xdx$

$-1/2lny=lnx+C$

Remember that any modification to $C$ is basically immaterial, it stays $C$ because it becomes some other unimportant constant:

$lny=-2lnx+C$

$y=e^(-2lnx+C$

$y=e^(-2lnx)*e^C$

$y=Ce^(ln(x^-2))$

$y=Cx^-2$

$y=C/x^2$

What is a solution to the differential equation xy' + 2y = 0xy' + 2y = 0?