?(Principle of superposition) Prove that if \(y_{1}(x)\) and \(y_{2}(x)\) are solutions
Chapter 7, Problem 52(choose chapter or problem)
(Principle of superposition) Prove that if \(y_{1}(x)\) and \(y_{2}(x)\) are solutions to a linear homogeneous differential equation, \(y^{\prime \prime}+p(x) y^{\prime}+q(x) y=0\), then the function \(y(x)=c_{1} y_{1}(x)+c_{2} y_{2}(x)\), where \(c_{1}\) and \(c_{2}\) are constants, is also a solution.
Text Transcription:
y_1 (x)
y_2 (x)
y^prime prime + p(x)y^prime + q(x)y = 0
y(x)=c_1 y_1 (x) + c_2 y_2 (x)
c_1
c_2
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