Question:
If \(y(x)\) is the solution of the differential equation \((x+2)\frac{dy}{dx} = x^2 + 4x - 9\), \(x \neq -2\) and \(y(0) = 0\), then \(y(-4)\) is equal to
If \(y(x)\) is the solution of the differential equation \((x+2)\frac{dy}{dx} = x^2 + 4x - 9\), \(x \neq -2\) and \(y(0) = 0\), then \(y(-4)\) is equal to
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Write \(x^2 + 4x - 9 = (x+2)^2 - 13\) and integrate \(\frac{dy}{dx} = (x+2) - \frac{13}{x+2}\).
Updated On: Nov 11, 2026
- \(-1\)
- \(1\)
- \(0\)
- \(2\)
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The Correct Option is C
Solution and Explanation
\(\frac{dy}{dx} = \frac{(x+2)^2 - 13}{x+2} = (x+2) - \frac{13}{x+2}\).
Integrating: \(y = \frac{(x+2)^2}{2} - 13\log|x+2| + C\).
\(y(0) = 0\): \(2 - 13\log 2 + C = 0\), so \(C = 13\log 2 - 2\).
\(y(-4) = \frac{4}{2} - 13\log 2 + 13\log 2 - 2 = 0\).
Answer: (3) \(0\)
Integrating: \(y = \frac{(x+2)^2}{2} - 13\log|x+2| + C\).
\(y(0) = 0\): \(2 - 13\log 2 + C = 0\), so \(C = 13\log 2 - 2\).
\(y(-4) = \frac{4}{2} - 13\log 2 + 13\log 2 - 2 = 0\).
Answer: (3) \(0\)
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