jee-main 2022 Q76

jee-main · India · session2_29jul_shift2 First order differential equations (integrating factor)

Let $y = y(x)$ be the solution curve of the differential equation $\frac{dy}{dx} + \frac{2x^2 + 11x + 13}{x^3 + 6x^2 + 11x + 6} y = \frac{x + 3}{x + 1}$, $x > -1$, which passes through the point $(0, 1)$. Then $y(1)$ is equal to
(1) $\frac{1}{2}$
(2) $\frac{3}{2}$
(3) $\frac{5}{2}$
(4) $\frac{7}{2}$

Let $y = y(x)$ be the solution curve of the differential equation $\frac{dy}{dx} + \frac{2x^2 + 11x + 13}{x^3 + 6x^2 + 11x + 6} y = \frac{x + 3}{x + 1}$, $x > -1$, which passes through the point $(0, 1)$. Then $y(1)$ is equal to\\
(1) $\frac{1}{2}$\\
(2) $\frac{3}{2}$\\
(3) $\frac{5}{2}$\\
(4) $\frac{7}{2}$

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