y'=(1+y^2)/(1+x^2) y(2)=3 book answer y=(x+c)/(1-cx) how is this possible with out trig substitution

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.

Get our expert's

answer on brainly

SEE EXPERT ANSWER

Get your free account and access expert answers to this and thousands of other questions.

A community for students.

y'=(1+y^2)/(1+x^2) y(2)=3 book answer y=(x+c)/(1-cx) how is this possible with out trig substitution

Mathematics
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
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.

Get this expert

answer on brainly

SEE EXPERT ANSWER

Get your free account and access expert answers to this and thousands of other questions

It's not. And the answer should remind you of this trig identity that will be very useful: \[ \tan(a+b) = \frac{ \tan a + \tan b}{1 - \tan a . \tan b} \]
y′=((1+y²)/(1+x²)), y(0)=3 Equation with separable variables: ((y′)/(1+y²))=(1/(1+x²))⇒arctan y=arctan x+C arctan y(0)=arctan0+C⇒arctan3=C arctan y=arctan x+arctan3 [this is the solution in implicit form... up to here the differential equation problem should be considered solved] To solve the implicit function problem, use the formula JamesJ gave you: ⇒y(x)=tan(arctan x+arctan3)=((x+3)/(1-3x)) Please note this is just the first-level solution ... strictly speaking, you still have to find the (maximal) domain of the solution, maybe discuss some other issues ...

Not the answer you are looking for?

Search for more explanations.

Ask your own question

Other answers:

Not the answer you are looking for?

Search for more explanations.

Ask your own question