(x^2 + 1)y' + 2xy^2 = 0
Denne likningen er i kapitllet med separable difflkninger, men jeg greier ikke få x'ene og y'ene alene
Difflikning
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Fibonacci92
- Abel
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[tex](x^2 + 1)y^\prime + 2xy^2 = 0 [/tex]
[tex](x^2 + 1)y^\prime = -2xy^2 [/tex]
[tex]\frac{(x^2 + 1)y^\prime }{(x^2 + 1)} = \frac{-2xy^2}{(x^2 + 1)}[/tex]
[tex] y^\prime = \frac{-2xy^2}{(x^2 + 1)}[/tex]
[tex] \frac{y^\prime}{y^2} = \frac{-2xy^2}{(x^2 + 1)y^2}[/tex]
[tex] \frac{y^\prime}{y^2} = \frac{-2x}{(x^2 + 1)}[/tex]
[tex](x^2 + 1)y^\prime = -2xy^2 [/tex]
[tex]\frac{(x^2 + 1)y^\prime }{(x^2 + 1)} = \frac{-2xy^2}{(x^2 + 1)}[/tex]
[tex] y^\prime = \frac{-2xy^2}{(x^2 + 1)}[/tex]
[tex] \frac{y^\prime}{y^2} = \frac{-2xy^2}{(x^2 + 1)y^2}[/tex]
[tex] \frac{y^\prime}{y^2} = \frac{-2x}{(x^2 + 1)}[/tex]