A differential equation Show that both of the following

QUESTION:

A differential equation Show that both of the following conditions are satisfied by

\(y=\sin x+\int_{x}^{\pi} \cos 2 t \quad d t+1\):

i.) \(y^{\prime \prime}=-\sin x+2 \sin 2 x\)

ii.) \(y=1 \text { and } y^{\prime}=-2 \text { when } x=\pi\).

Equation Transcription:

Text Transcription:

y = sin x + integral_x^pi cos 2t dt+1

y’’ = -sin x + 2 sin 2x

y = 1 and y’ = -2 when x = pi