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**Unformatted text preview: **, ). 3. Since y = sin x + x 2 , we have y = cos x + 2 x and y = sin x + 2. These unctions are defned on ( , ). Substituting these expressions into the dierential equation y + y = x 2 + 2 gives y + y = sin x + 2 + sin x + x 2 = 2 + x 2 = x 2 + 2 or all x in ( , ) . Thereore, y = sin x + x 2 is a solution to the dierential equation on the interval ( , ). 5. Dierentiating x ( t ) = cos 2 t , we get dx dt = d dt (cos 2 t ) = ( sin 2 t )(2) = 2 sin 2 t. 4...

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