(adsbygoogle = window.adsbygoogle || []).push({}); Hi, everyone. Don’t know how to solve (x^2-1)y"+xy'-y=0

Which books are nice discussing about this kind of differential equations?

Many many thanks

A1. [itex]y\prime=\frac{4x^2}{y}+\frac{y}{x}[/itex]

Ans: [itex]y=2x \sqrt{2x+3}[/itex]

A2. [itex]y\prime=\frac{2y}{x}-\frac{x^4}{2y}[/itex]

Ans: [itex]y=x^2 \sqrt{1-x}[/itex]

B1. [itex](1+x^2)y\prime\prime+3x y\prime =0[/itex]

Ans: [itex]y=\frac{x}{\sqrt{1+x^2}}[/itex]

B2. [itex](x^2-1)y\prime\prime +x y\prime-y=0[/itex]

Ans: [itex]y=x+ \sqrt{x^2-1}[/itex]

B3. [itex]y\prime\prime +\frac{2}{x} y\prime +y=0[/itex]

Ans: [itex]y=\frac{\cos{x}}{x}[/itex]

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# (x^2-1)y +xy'-y=0 Don’t know how to solve. Which books are nice discussing about this

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