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xenn [34]
3 years ago
6

Solve the differential equations dy/dx=((xy^2)+x)/y

Mathematics
1 answer:
arsen [322]3 years ago
7 0

\displaystyle \dfrac{dy}{dx}=\dfrac{xy^2+x}{y}\\ \dfrac{dy}{dx}=\dfrac{x(y^2+1)}{y}\\ \dfrac{y}{y^2+1}\, dy=x\, dx\\ \int \dfrac{y}{y^2+1}\, dy=\int x\, dx\\ \dfrac{\ln (y^2+1)}{2}=\dfrac{x^2}{2}+C\\ \ln(y^2+1)=x^2+C\\ y^2+1=e^{x^2+C}\\ y^2=e^{x^2+C}-1\\ y=\sqrt{e^{x^2+C}-1} \vee y=-\sqrt{e^{x^2+C}-1}\\ \boxed{y=\sqrt{Ce^{x^2}-1} \vee y=-\sqrt{Ce^{x^2}-1}}\\

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sveta [45]

Answer:

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Step-by-step explanation:

The scale of a map is 1:10000

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This scale means that for every 1 meter on the map there are 10,000 meters on the real world.

So 600 meters on the real world would be represented by;

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