Question

Find the solution to the initial value problem. y⁻³ θ-4 y=sin θ (2 )-4 e^{3 } ; y(0)=1, y³(0)=____ ; y=______

Answer 1

Unable to solve the initial value problem due to typographical errors in the provided equation. Correct steps include identifying knowns and choosing the right equation.

Step-by-step explanation:

The question provided has some typographical errors and is incomplete, making it challenging to offer an accurate solution to the initial value problem presented. However, assuming we correct the typos and the equation resembles a typical differential equation we would proceed by solving the differential equation using appropriate methods such as separation of variables or an integrating factor, depending on the corrected form of the equation.

Once we have the general solution to the differential equation we would apply the initial value,
`y(0)=1`, to find the particular solution that satisfies this condition.

If the third derivative is needed,
`y³(0)`, this would typically involve differentiating the solution found and evaluating it at
`θ=0`.

Unfortunately without the correct equation, we cannot execute these steps in this case. Nevertheless it's essential to first identify the knowns and then choose the equation that allows solving for the unknowns using these values as initially indicated.