Maryfayemiwoidn
Answered

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Solve the equation (1 + x²)dy +xydx= 0​

Sagot :

Really226idn

Answer:

[tex]y=\frac{c}{\sqrt[]{x^2+1} }[/tex]

Step-by-step explanation:

(1 + x²)dy +xydx= 0​

[tex](1+x^2)dy=-xydx\\\frac{1}{y}dy=\frac{-x}{x^2+1}dx\\[/tex]

Integrate both side

[tex]lny=-\frac{1}{2} ln(x^2+1)+c\\y=\frac{c}{\sqrt[]{x^2+1} }[/tex]

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