Hi everyone!
Have been trying to solve this equation for a while, but just cannot find the right way. Could you, please, help on this one? Thanks!
\(\displaystyle \color{black}{\dfrac{x^{n-1}\, -\, y(x)^{n-1}}{n\, -\, 1}\, -\, \dfrac{x^{n-2}\, -\, y(x)^{n-2}}{n\, -\, 2}p\, =\, \dfrac{1}{2}y(x)^{n-3}\left(p\, -\, y(x)\right)^2\,y'(x)}\)
\(\displaystyle \color{black}{\mbox{Where }\, n\, \geq\, 3\, \mbox{ and }\, 0\, <\, p\, <\, x\, <\, 1,\, n,\, p\, -\, \mbox{ parameters.}}\)
Have been trying to solve this equation for a while, but just cannot find the right way. Could you, please, help on this one? Thanks!
\(\displaystyle \color{black}{\dfrac{x^{n-1}\, -\, y(x)^{n-1}}{n\, -\, 1}\, -\, \dfrac{x^{n-2}\, -\, y(x)^{n-2}}{n\, -\, 2}p\, =\, \dfrac{1}{2}y(x)^{n-3}\left(p\, -\, y(x)\right)^2\,y'(x)}\)
\(\displaystyle \color{black}{\mbox{Where }\, n\, \geq\, 3\, \mbox{ and }\, 0\, <\, p\, <\, x\, <\, 1,\, n,\, p\, -\, \mbox{ parameters.}}\)
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