UnkleRhaukus 5 years ago $x^3y'+3y^2=xy^2$

1. myininaya

$\frac{dy}{dx} \cdot x^3=y^2(x-3)$

2. myininaya

$\frac{1}{y^2} dy=\frac{x-3}{x^3} dx$

3. myininaya

integrate both sides

4. myininaya

$\int\limits_{}^{}y^{-2} dy =\int\limits_{}^{}(x^{-2}-3x^{-3}) dx$

5. myininaya

$\frac{y^{-2+1}}{-2+1}=\frac{x^{-2+1}}{-2+1}-3 \cdot \frac{x^{-3+1}}{-3+1}+C$

6. myininaya

$-\frac{1}{y}=\frac{-1}{x}-3\frac{1}{-2x^{2}}+C$

7. myininaya

$\frac{-1}{y}=\frac{-1}{x}+\frac{3}{2x^2}+C$

8. myininaya

it was just separation by variables

9. UnkleRhaukus

thankyou myininaya, i could not see that is was just separation of variable. but the answer in my text has arctans and lns, i guess i need to rearrange a negative before integration

10. myininaya

that is the right problem right?

11. myininaya

thats weird to me that it would have arctans and lns

12. UnkleRhaukus

13. myininaya

lol

14. myininaya

:)

15. myininaya

goodnight unkle great job on explaining fourier to matt

16. UnkleRhaukus

it is 3 in the afternoon to me, but good night anyway, thanks