?Find the unique solution satisfying the differential equation and the initial
Chapter 7, Problem 81(choose chapter or problem)
Find the unique solution satisfying the differential equation and the initial conditions given, where \(y_{p}(x)\) is the particular solution.
\(y^{\prime \prime}-7 y^{\prime}=4 x e^{7 x}\) , \(y_{p}(x)=\frac{2}{7} x^{2} e^{7 x}-\frac{4}{49} x e^{7 x}\)
y(0) = -1, \(y^{\prime}(0)=0\)
Text Transcription:
y_p(x)
y^prime prime-7y^prime=4xe^7x
y_p(x)=2/7 x^2 e^7x - 4/49 xe^7x
y^prime (0)=0
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