GATE (TF) Textile 2018 Question Paper Solution | GATE/2018/TF/21

Question 21 (Textile Technology & Fibre Science)

If $y(x)$ is the solution of the differential equation $yy'=8x$ , $y(0=2)$ , then the absolute value of $y(2)$ is __6__.

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$yy'=8x$
$y\frac{dy}{dx}=8x$
$\int y dy=8 \int x dx$
$\frac{y^2}{2}=8\frac{x^2}{2}+c$
$y^2=8x^2+2c$
$y(0)=2$ i.e. y=2 when x=0
c=2
$y^2=8 \times x^2+4$
$y^2=8 \times (2)^2+4$
$y^2=8 \times 4+4$
$y^2=32+4$
$y^2=36$
$y=\sqrt 36$
y=6 (Ans)

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