In 13 and 14 the given two-parameter family is a solution

QUESTION:

In Problems 13 and 14 the given two-parameter family is a solution of the indicated differential equation on the interval \((-\infty,)\). Determine whether a member of the family can be found that satisfies the boundary conditions

\(y=c_{1} e^{x} \cos x+c_{2} e^{x} \sin x ; \quad y^{\prime \prime}-2 y^{\prime}+2 y=0\)

(a) \(y(0)=1, \quad y^{\prime}(\pi)=0\)

(b) \(y(0)=1, \quad y(\pi)=-1\)

(c) \(y(0)=1, \quad y(\pi / 2)=1\)

(d) \(y(0)=0, \quad y(\pi)=0\).

Text Transcription:

-infty

y=c_{1} e^{x} \cos x+c_{2} e^{x} \sin x ; \quad y^{\prime \prime}-2 y^{\prime}+2 y=0

y(0) = 1, y(p) = 0

y(0) = 1, y(p) = 1

y(0) = 1, y(p2) = 1

 y(0) = 0, y(p) = 0