Question

If $\frac{dy}{dx}=x^2+1$ and $y=12$ when $x=3$. Then the function is:

• A. $3(y+x)=x^3$
• B. $3(y-x)=x^3$
• C. $(y+x)=x^3$
• D. $(y-x)=x^3$

Answer 1

Answer: (B)

$3(y-x)=x^3$

Given, $\frac{dy}{dx}=x^2+1$

Thus $dy=(x^2+1)dx$
$\Rightarrow y=\frac{x^3}{3}+x+c$
Also given, $(x,y)=(3,12)$
$\Rightarrow 12=9+3+c$
$\Rightarrow c=0$
Therefor,e the function is $3y=x^3+3x$
$\Rightarrow 3(y-x)=x^3$