Question

(Equation Coming Soon) Determine whether the given relation is an implicit solution to the given differential equation. Assume that the relationship does define y implicitly as a function of x and use implicit differentiation.

Answer 1

\[y- \ln y = x ^{2}+1\]\[\frac{ dy }{ dx }=\frac{ 2xy }{ y-1 }\]

Answer 2

implicit differentiation, from my understanding means set the above equation to 0 and differentiate it. If it matches the below equation then it is a solution.

Answer 3

@Hero @TuringTest DIff EQ Help

Answer 4

no setting to zero, it means when you differentiate a function of y wrt x you use the chain rule

Answer 5

for example
y^2=x+y
derivative implicit wrtx is
(2y)y'=1+y'
we could solve this for the derivative y', which is what they want you to do

Answer 6

can you briefly refresh me on the chain rule.

Answer 7

ok

Answer 8

\[\frac{ dy }{ dx }-\frac{ 1 }{ y }\frac{ dy }{ dx }=2x\]?

Answer 9

for compound functions like\[(3x+1)^2\]the derivative requires the chain rule
derivative of outside function times derivative of inside function\[2(3x+1)(3)\]and yes to your attempt

Answer 10

so\[\frac{ dy }{ dx }(1-\frac{ 1 }{ y })=2x\]i did get this far on my own but I can't seem to get it to match the differential equation above. The book says it should be a solution.

Answer 11

it's just algebra dude, get a common denominator :P

Answer 12

I think I am fogetting some basic algebra when dividing

Answer 13

\[1\frac yy=\frac yy\]

Answer 14

got it. im embarassed. Forgot the easy stuff when working with the hard stuff. unforgivable

Answer 15

it happens to the best of us ;)