Question

The solution of the differential equation dy/dx + 2y/x=0 with y(1)=1 is given by.......,Select correct option from given options.
(a) y=1/x
(b) y=1/x²
(c) x=1/y²
(d) x²=1/y²

Answer 1

Answer:

The solution is

$y=\frac{1}{x^{2}}$

option (2) is correct

Step-by-step explanation:

The solution of the differential equation dy/dx + 2y/x=0 with y(1)=1 is given by.......,Select correct option from given options.

I have applied variable separable method to solve this problem

$\frac{dy}{dx}+\frac{2y}{x}=0$

$\frac{dy}{dx}=\frac{-2y}{x}$

separating the variables

$\frac{dy}{y}=\frac{-2\:dx}{x}$

Integrating both sides

$\int\frac{dy}{y}=-2\int\frac{dx}{x}$

$logy=-2\:logx+c$..........(1)

But when x=1, y=1

$log\;1=-2\:log\:1+c$

$0=-2(0)+c$

$\implies\:c=0$

(1) becomes

$logy=-2\:logx$

$logy=logx^{-2}$

$\implies\:y=x^{-2}$

$\implies\:\boxed{y=\frac{1}{x^{2}}}$