Question

The solution of the differential equation 2x dy/dx -y =0; y(1)=2 represents........,Select correct option from given options.
(a) straight line
(b) parabola
(c) circle
(d) ellipse

Answer 1

Answer:

Solutioion of the given differential equation represents a parabola

option (b) is correct

Step-by-step explanation:

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

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

separating the variables, we get

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

Integrating on both sides we get

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

$2\:log\:y=logx+logc$

$log\:y^2=log\:xc$

$y^2=xc$ .........(1)

when x=1, y=2

$2^2=(1)c$

$\implies\:c=4$

(1) becomes

$y^2=4x$

This equation repressents a parabola