Question

If \[ \frac{dy}{dx} - \frac{2x}{x^2+b}y = -2x(x^2+b), \] with \[ y(0)=12,\qquad y(1)=10, \] then the sum of all possible values of \(b\) is:

• A. \(1\)
• B. \(4\)
• C. \(-3\)
• D. \(-1\)

Hint:

For linear differential equations, always compute the integrating factor first. It converts the left-hand side into an exact derivative.

Answer 1

The Correct Option is A