anonymous
  • anonymous
Solve the seperable differential equation for. \frac(dy)(dx) = \frac(1+x)(xy^(6)) ; \ \ x \gt 0 Use the following initial condition: y(1) = 5 .
Mathematics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
jamiebookeater
  • jamiebookeater
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
zepdrix
  • zepdrix
\[\Large \frac{dy}{dx}=\frac{1+x}{xy^6}, \qquad\qquad x\gt0, \qquad\qquad y(1)=5\]
zepdrix
  • zepdrix
What part are you stuck on maria? :o Understand the separation portion of it?\[\Large y^6\;dy=\frac{1+x}{x}\;dx\]
anonymous
  • anonymous
No I don't!!! I forgot ittt

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

zepdrix
  • zepdrix
\[\Large \frac{dy}{dx}=\frac{1+x}{xy^6}\]So we want all of our `y and dy` on one side of the equation with all of our `x and dx` on the other side :o So we start by multiplying both sides by y^6.\[\Large y^6\frac{dy}{dx}=\frac{1+x}{x}\]Right? +_+
anonymous
  • anonymous
so what do I have to plug in to get y=? because that part makes sense I just don't know how to use that information further
zepdrix
  • zepdrix
You need to integrate which will get rid of the differentials. Have you done that part yet? :o\[\Large \int\limits y^6\;dy=\int\limits \frac{1+x}{x}\;dx\]
anonymous
  • anonymous
1/7y^7=(ln|x|)+x
zepdrix
  • zepdrix
\[\Large \frac{1}{7}y^7=\ln|x|+x+C\] Ok good :) Now we can use our initial condition solve for our unknown constant.
zepdrix
  • zepdrix
\[\Large y(1)=5\]Plugging in gives us,\[\Large \frac{1}{7}5^7=\ln|1|+1+C\]
anonymous
  • anonymous
11160.71=10.320155+c
zepdrix
  • zepdrix
Nooo, no decimals! :O And what happened on the right side there..? Recall: ln1=0
anonymous
  • anonymous
111.60.71=1+C
anonymous
  • anonymous
11160=C
zepdrix
  • zepdrix
fine fine fine :) have your sloppy decimals lol that looks good. So now we plug our c back in. and since we're able to, we should probably solve for y.
zepdrix
  • zepdrix
\[\Large \frac{1}{7}y^7=\ln|x|+x+11160\]
zepdrix
  • zepdrix
\[\Large y=?\]

Looking for something else?

Not the answer you are looking for? Search for more explanations.