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03-04-2020
Mathematics

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is y=x^3 a solution of the differential equation yy'=x^5+y

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LammettHash LammettHash

16-04-2020

No; we have [tex]y=x^3\implies y'=3x^2[/tex]. Substituting these into the DE gives

[tex]3x^5=x^5+x^3[/tex]

which reduces to [tex]x^3=0[/tex], true only for [tex]x=0[/tex].

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