Consider the ordinary differential equation (ODE) d^2y/dx^2+(cos x)dy/dx+(sin x),y=0. Let varphi1(x),varphi2(x) be solutions of the ODE, satisfying varphi1(0)=1, dvarphi1/dx(0)=0,quadandquadvarphi2(0)=0, dvarphi2/dx(0)=1. Then which of the following statements are true?

Q92Section C (Part C)92 of 120

Solutions of a linear ODE with $2\pi$ -periodic coefficients

Consider the ordinary differential equation (ODE)

$\frac{d^2y}{dx^2}+(\cos x)\frac{dy}{dx}+(\sin x)\,y=0.$

Let $\varphi_1(x),\varphi_2(x)$ be solutions of the ODE, satisfying

$\varphi_1(0)=1, \frac{d\varphi_1}{dx}(0)=0,\quad\text{and}\quad\varphi_2(0)=0, \frac{d\varphi_2}{dx}(0)=1.$

Then which of the following statements are true?

Multiple select: one or more options are correct. Select all of them, then submit — marks need the exact set.

Select every correct option, then submit.

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