Question

The solution of \[ \frac{dy}{dx} + \left[2(x-1)\sin x+x(x-2)\cos x\right]y = \frac{e^{2x\sin x}}{e^{x^2\sin x}}, \] at \(x=2\) if \(y(\pi)=0\) is

• A. \(2-\pi\)
• B. \(\dfrac{\pi}{2}\)
• C. \(\pi+2\)
• D. \(\pi^2\)

Hint:

For a linear differential equation, \[ \boxed{ \frac{dy}{dx}+P(x)y=Q(x) } \] the integrating factor is \[ \boxed{ e^{\int P(x)\,dx}. } \] Always check whether \(P(x)\) is the derivative of a known expression.

Answer 1

The Correct Option is A