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

7 0

3 years ago

Least common denominator between the fractions 1/3 and 2/8

Mekhanik [1.2K]

Answer:

LCD 1

Step-by-step explanation:

4 0

2 years ago

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Can someone please turn this into a equation and then solve it plz it’s due tommorow

jeka57 [31]

If the perimeter is 28 units, then you know you will have to add the same four numbers to get the perimeter. What times 4 can get you to 28? 7. 7 x 4=28. So what plus 3 gets us to 7? 4. The answer is 4, or x=4.

5 0

3 years ago

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What adds up to -11 but multiplies to 10?

xxMikexx [17]

The answer is -1 and -10

7 0

2 years ago