Question: Solve the initial value problem: [ begin{array}{} frac{d^{4} y}{d x^{4}}=y^{(4)}(x)=-cos x+8 sin 2 x y^{prime prime prime}(0)=0, y^{prime prime}(0)=y(0)=1, y(0)=3 end{array} ]

$Solve the initial value problem: \[ \begin{array}{} \frac{d^{4} y}{d x^{4}}=y^{(4)}(x)=-\cos x+8 \sin$

Solve the initial value problem: \[ \begin{array}{} \frac{d^{4} y}{d x^{4}}=y^{(4)}(x)=-\cos x+8 \sin 2 x \\ y^{\prime \prime \prime}(0)=0, y^{\prime \prime}(0)=y(0)=1, y(0)=3 \end{array} \]

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