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alliegator
Group Title
"Consider equation
x^2y''2xy'+2y=0, x>0
What differential equation does the Wronskian W(x)=W[y1,y2](x) for any pair of solutions of the above equation satisfy?"
 2 years ago
 2 years ago
alliegator Group Title
"Consider equation x^2y''2xy'+2y=0, x>0 What differential equation does the Wronskian W(x)=W[y1,y2](x) for any pair of solutions of the above equation satisfy?"
 2 years ago
 2 years ago

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across Group TitleBest ResponseYou've already chosen the best response.1
Abel's theorem states that if \(y_1(x)\) and \(y_2(x)\) are two solutions to\[y''+p(x)y'+q(x)y=0,\]then the Wronskian of the two solutions is\[W(y_1,y_2)(x)=c\exp\left[\int p(x)\,dx\right].\]For this case, we have that \(p(x)=2/x\). Hence\[W(y_1,y_2)(x)=cx^2.\]
 2 years ago
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