[tex]\acute{y}+xy^{3}+\frac{y}{x}=0[/tex](adsbygoogle = window.adsbygoogle || []).push({});

[tex]y(1)=2[/tex]

using substitution [tex]u=y^{-2}[/tex]

[tex]e^{y}\acute{y}=e^{-x}-e^{y}[/tex]

[tex]y(0)=0[/tex]

using substitution [tex]u=e^{y}[/tex]

i could not make these equations seperable and solve for the IVP.

Anyone has any idea?

Edit: these problems are not homework, but for self study for preparation to the midterm.

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# Substitution to make it seperable

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