Teaching MPPSC Assistant Professor Mock Test Series 2025 Mathematical Science Ordinary Differential Equations
On the open interval (−c, c), where c is a positive real number, y(x) is an infinitely differentiable solution of the differential equation \(\frac{d y}{d x}=y^{2}-1+\cos x\) with the initial condition y(0) = 0. Then which one of the following is correct?
1
y(x) has a local maximum at the origin.
2
y(x) has a local minimum at the origin.
3
y(x) is strictly increasing on the open interval (−δ, δ) for some positive real number δ.
4
y(x) is strictly decreasing on the open interval (−δ, δ) for some positive real number δ.