Question

A differential equation is given by $y\frac{dy}{dx}=(x+sinx)$, if y(0)=0, then the value of y(2) is _______(Answer upto two decimal places).

• A. 2.614

Answer 1

The correct option is A 2.614
Given, $y\frac{dy}{dx}=x+sinx$

$\Rightarrow$ $\int ydy=\int (x+sinx)dx$

$\Rightarrow$ $\frac{y^2}{2}=\frac{x^2}{2}-cosx+c$

Given, y(0) = 0,

$\Rightarrow 0=0-1+c$
$\Rightarrow c=1$

Now, y(2),

$\frac{y^2}{2}=\frac{2^2}{2}-cos2+1$
$\Rightarrow \frac{y^2}{2}=3-cos2$
$\Rightarrow y=2.614$