Note: WeBWorK will interpret acos(x) as $\cos^{-1}(x)$, you need to type a*cos(x) or put a space between them.

One of the following is a general solution of the homogeneous differential equation $y^{\prime\prime}+y=0$
$$\begin{aligned} y&=a e^{x}+b e^{-x} \\ y&=a x+b \\ y&=a\cos\!\left(x\right)+b\sin\!\left(x\right) \\ \end{aligned}$$ and one of the following is a solution to the nonhomogeneous equation $y^{\prime\prime}+y=\sec(x)$ $$\begin{aligned} y&= x\sin(x)\\ y&=x\sin\!\left(x\right)+\cos\!\left(x\right)\ln\!\left(\cos\!\left(x\right)\right) \\ \end{aligned}$$ By superposition, the general solution of the equation $y^{\prime\prime}+y=\sec(x)$ is
$y =$
Find the solution with
$$\begin{aligned} y(0)&=3 \\ y^\prime(0)&=6 \\ \end{aligned}$$ $y =$

The Wronskian of the general solution (using only the solutions to the homogeneous equation without the coefficients a and b) is . The fundamental theorem says that this solution is the unique solution to the IVP on the interval