Castiel
  • Castiel
Third order linear differential equation
Mathematics
chestercat
  • chestercat
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Castiel
  • Castiel
\[y _{1}=-x ^{2}\] \[y _{2}(x)=3x ^{2}lnx\] are solutions to \[y \prime \prime \prime +p(x)y \prime \prime+g(x)y \prime=0 \] \[x>0\] Is \[y(x)=2x ^{2}-10x ^{2}lnx\] a solution to equation?
Castiel
  • Castiel
How do I test that, I know that if y(x) is a solution then Cy(x), C being any real number is also a solution, and if y1(x) and y2(x) are solutions then y1(x)+y2(x) is also a solution. But is there something I'm missing?
Castiel
  • Castiel
If something isn't a solution how do I show it isn't a solution?

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Castiel
  • Castiel
Wait, if Cy(x) can be a solution and two solutions also give a solution then can I write -10/3 * y2 as one solution and -2*y1 as another and adding those two we get y(x) as above. We just proved it is a solution?

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