# Calculus

posted by .

dy/dx= (y^2 -1)/x

1. Give the general equation of the curves that satisfy this equation.

2. Show that the straight lines y=1 and y=-1 are also solutions.

3. Do any of the curves you found in 1) intersect y=1?

i started by
dy/(y^2 -1)= dx/x
and found that
[ln(y-1) - ln(y+1)]/2 = lnx

what do i do next?

The left becomes
ln((y-1)/(y+1))
move the 2 to the right to make 2lnx or lnx^2

When y is +- 1, what is the slope? Is it that slope for all x? If so, it is a straight line.

so x^2 + C = (y-1)/(y+1) is the general equation?

how do i show that the straight lines y=1 and y=-1 are also solutions.

## Similar Questions

dy/dx= (y^2 -1)/x 1. Give the general equation of the curves that satisfy this equation. 2. Show that the straight lines y=1 and y=-1 are also solutions 3. Do any of the curves you found in 1) intersect y=1?
2. ### Math

The graph of the equation y=4-x consists of all the points in the coordinate plane that satisfy the equation. List 5 points that satisfy y= 4-x. Also, what do you think is the minimum number of points you need to plot in order to draw …
3. ### CountIblis, can i bother you

Countiblis, i know that you might be busy do you mind if i ask you the following for help.Only if you can please. can you explain to me just one more thing so i can undestand it. Now i have an equation which is : 3x = 3x + 5 which …
4. ### Math

Give an ordered pair (a,b) of numbers that satisfy the equation. I got (1,1) but cant i also be (2,4)?
5. ### Maths

Hi, need a bit of help on this one. A straight line passes through the points (4,3) and (10,0), I need to write down the equation of the line in the form y=mx+c, I have tried but I cant seem to get the second coordinates to satisfy …
6. ### calculus

two curves are orthogonal at a point of intersection of their tangents at that point cross at right angles. Show that the curves 2x^2+3y^2=5 and y^2=x^3 are orthogonal at (1,1) and (1,-1). Use parametric mode to draw the curves and …
7. ### Calculus 3

Given the function f(x,y)=y/(x^2+y^2), give and identify the level curves for k=1, k=1/2, and k=1/4, and draw a contour map showing these level curves. Any help would be immensely appreciated. Thanks
8. ### CALCULUS

Sketch the region enclosed by the given curves. y = 4/X y = 16x, y = 1X/16 x > 0 and the area between the curves
9. ### Calculus

Consider the differential equation dy/dx=xy-y. Find d^2y/dx^2 in terms of x and y. Describe the region in the xy plane in which all solutions curves to the differential equation are concave down.
10. ### Math

In this problem we consider drawing some straight lines which form a nice pattern. Consider joining the point (0.1,0) to the point (0,0.9) by a line segment; then joining (0.2,0) to (0,0.8) by a line segment; and so on. In general, …

More Similar Questions