JEE Main 2015 · 10 Apr · Shift 1 · Mathematics Q77

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MathematicsSingle correct+4 / -1Question 77 of 90

If $y(x)$ is the solution of the differential equation $(x+2)\dfrac{dy}{dx}=x^2+4x-9$ , $x\ne-2$ and $y(0)=0$ , then $y(-4)$ is equal to :

−1

Answer and worked solution

Official answer: A

$\dfrac{dy}{dx}=\dfrac{(x+2)^2-13}{x+2}=x+2-\dfrac{13}{x+2}$ . So
$y=\frac{(x+2)^2}2-13\ln|x+2|+c,$
and $y(0)=0$ gives $c=-2+13\ln2$ . At $x=-4$ : $y=2-13\ln2-2+13\ln2=0$ .

Topics:Variable separable

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JEE Main 2015 · 10 Apr · Shift 1, Mathematics question 77