Question:medium
If the solution of the differential equation \(\frac{dy}{dx} = \frac{\alpha x^2 + 4x - 4}{2y - 4}\), when \(y(1) = 3\), is \(y^2 - 4y = x^3 + 2x^2 - 4x + c\), then the value of \(\alpha\) is equal to
If the solution of the differential equation \(\frac{dy}{dx} = \frac{\alpha x^2 + 4x - 4}{2y - 4}\), when \(y(1) = 3\), is \(y^2 - 4y = x^3 + 2x^2 - 4x + c\), then the value of \(\alpha\) is equal to
Show Hint
In questions where the solution form is given, you don't always need to solve for the constant \(c\) unless specifically asked. Focus on equating the coefficients of corresponding powers of \(x\) or \(y\).
Updated On: Jun 24, 2026
- 1
- -1
- -3
- 3
Show Solution
The Correct Option is D
Solution and Explanation
Was this answer helpful?
0
Top Questions on Differential equations
- The solution of the differential equation \( x \cos y \, dy = (x e^x \log x + e^x) \, dx \) is:
- MHT CET - 2024
- Mathematics
- Differential equations
- The particular solution of the differential equation \(e \frac{dy}{dx} = (x + 1)\), \(y(0) = 3\), is:
- MHT CET - 2024
- Mathematics
- Differential equations
- If the curve \(y^2 = 6x\) and \(9x^2 + by^2 = 16\) intersect each other at right angles, then the value of \(b\) is:
- MHT CET - 2024
- Mathematics
- Differential equations
- The maximum value of \(\frac{\log(x)}{x}\) is:
- MHT CET - 2024
- Mathematics
- Differential equations
- Want to practice more? Try solving extra ecology questions todayView All Questions
