UnkleRhaukus
  • UnkleRhaukus
\[x^3y'+3y^2=xy^2\]
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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myininaya
  • myininaya
\[\frac{dy}{dx} \cdot x^3=y^2(x-3)\]
myininaya
  • myininaya
\[\frac{1}{y^2} dy=\frac{x-3}{x^3} dx\]
myininaya
  • myininaya
integrate both sides

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myininaya
  • myininaya
\[\int\limits_{}^{}y^{-2} dy =\int\limits_{}^{}(x^{-2}-3x^{-3}) dx\]
myininaya
  • myininaya
\[\frac{y^{-2+1}}{-2+1}=\frac{x^{-2+1}}{-2+1}-3 \cdot \frac{x^{-3+1}}{-3+1}+C\]
myininaya
  • myininaya
\[-\frac{1}{y}=\frac{-1}{x}-3\frac{1}{-2x^{2}}+C\]
myininaya
  • myininaya
\[\frac{-1}{y}=\frac{-1}{x}+\frac{3}{2x^2}+C\]
myininaya
  • myininaya
it was just separation by variables
UnkleRhaukus
  • 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
myininaya
  • myininaya
that is the right problem right?
myininaya
  • myininaya
thats weird to me that it would have arctans and lns
UnkleRhaukus
  • UnkleRhaukus
im sorry apparently i dont know how to read, your answer is perfect
myininaya
  • myininaya
lol
myininaya
  • myininaya
:)
myininaya
  • myininaya
goodnight unkle great job on explaining fourier to matt
UnkleRhaukus
  • UnkleRhaukus
it is 3 in the afternoon to me, but good night anyway, thanks

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