(a) Given that y = sin x is a solution of find the general
Chapter , Problem 32RP(choose chapter or problem)
(a) Given that y = sin x is a solution of
\(y^{(4)}+2 y^{\prime \prime \prime}+11 y^{\prime \prime}+2 y^{\prime}+10 y=0\),
find the general solution of the DE without the aid of a calculator or a computer.
(b) Find a linear second-order differential equation with constant coefficients for which \(y_{1}=1\) and \(y_{2}=e^{-x}\) are solutions of the associated homogeneous equation and \(y_{p}=\frac{1}{2} x^{2}-x) is a particular solution of the nonhomogeneous equation.
Text Transcription:
y^(4)+2 y^prime\prime\prime+11y^prime\prime+2y^prime+10y=0
y_1=1
y_2=e^-x
y_p=frac12x^2-x
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