Posted by **sammy** on Monday, May 19, 2008 at 3:25am.

consider the differential equation dy/dx= (y - 1)/ x squared where x not = 0

a) find the particular solution y= f(x) to the differential equation with the initial condition f(2)=0

(b)for the particular solution y = F(x) described in part (a) find lim F(x) X goes to infinity

- calculus -
**drwls**, Monday, May 19, 2008 at 6:32am
dy/dx = (y - 1)/ x^2

Use the integration method of separation of variables.

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

ln (y-1) = -1/x + C

You say that the initial condition is

f(x) = y = 0 at x =2

Are you sure the initial condition is not f(0) = 2 ? You cannot have a logarithm of a negative number.

- calculus -
**alame**, Tuesday, March 16, 2010 at 6:27pm
Start like above, but once you gget to the logarithm part, it is in absolute values, so it is ln(1) which is 0. Solve from there

- calculus -
**Andy**, Saturday, March 19, 2011 at 2:56pm
The two statements above is wrong.

you first move around the

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

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

Then you integral where it turns to

ln( (y-1)/C ) = -1/x

Next you move the e from the ln to the other side

(y-1)/C = e^(-1/x)

After that you times C to both sides and move the -1 afterwords

y-1 = Ce^(-1/x) --> y = Ce^(-1/x)+1

I not sure how you do part (b) though.

Sorry

## Answer This Question

## Related Questions

- Calculus!! - Consider the differential equation given by dy/dx = xy/2. A. Let y=...
- calculus-differential equation - Consider the differential equation: (du/dt)=-u^...
- calculus - verify that y=c/x^2 is a general solution of the differential ...
- Calculus - 1)Find the particular solution of the differential equation xy'+3y=...
- ap calculus - find the particular solution y=f(x) to the differential equation ...
- calculus - Find the domain for the particular solution to the differential ...
- Calculus - Find the particular solution of the differential equation y'=(5x+21y...
- Calculus - Consider the differential equation, dy/dx=(x+1)/y^2 with the initial ...
- ap calculus - let y=f(x) be the particular solution for the differential ...
- Calculus - Solve the separable differential equation: dy/dt=4y^6 and find the ...

More Related Questions