eqn of tangent to y^2 + ln(xy) = 2; solve diffEQ

[mbcool318]

I WAS GIVEN THESE 2 QUESTION BY SOMEONE AND I NEED THE ANSWER PLEASE HELP...

Question
1) Find the equation of the tangent line to the graph: y^2 + ln(xy) = 2
at the point (e, 1)

2) Solve the differential equation: dy/dx= 4/(9+x^2) given the initial condition y(0)=3

 

[pka]

Re: HELP! y^2 + ln(xy) = 2

I WAS GIVEN THESE 2 QUESTION BY SOMEONE AND I NEED THE ANSWER PLEASE HELP...

Why not let that "someone" do his/her own work?
Why are you doing it?

 

[stapel]

1) Differentiate implicitly. Plug in the given x- and y-values. Solve for "(dy/dx)=", since this is the slope at the point.

Then use what you learned back in algebra to find the line equation, now that you have the slope and a point.

2) Integrate dy/dx with respect to x, in order to find y. Use the listed initial condition to solve for the value of the constant of integration.

If you get stuck, please reply showing how far you have gotten. Thank you.

Eliz.

 

[tkhunny]

One would be wise to check that the point is actually ON the given curve. It's very embarrassing when it isn't.