Solve the initial value problem:

(dy/dx) = (y+1(x-1)) ; y(1)=3 variable separable

We've only recently began the unit on Integration applications and Differentials, so I have absolutely no idea how to approach this. If any of you can show me how to solve this, it would be most appreciated.

Re: Solve the initial value problem:

Quote:

Originally Posted by

**andvaka** (dy/dx) = (y+1(x-1)) ; y(1)=3 variable separable

We've only recently began the unit on Integration applications and Differentials, so I have absolutely no idea how to approach this. If any of you can show me how to solve this, it would be most appreciated.

Separating the variables we get dy/(y+1)=(x+1)dx Integrate both sides log (y+1)= x^2/2+x+C

When x=1 y=3 so log4=(1/2)+1+C So C=log4-3/2 etc.

Re: Solve the initial value problem:

Quote:

Originally Posted by

**biffboy** Separating the variables we get dy/(y+1)=(x+1)dx Integrate both sides log (y+1)= x^2/2+x+C

When x=1 y=3 so log4=(1/2)+1+C So C=log4-3/2 etc.

Shouldn't the (x+1)dx in "dy/(y+1)=(x+1)dx" be (x-1)dx . or is there a reason for the sign change?

Thanks.

Re: Solve the initial value problem:

Quote:

Originally Posted by

**andvaka** (dy/dx) = (y+1(x-1)) ; y(1)=3 variable separable

We've only recently began the unit on Integration applications and Differentials, so I have absolutely no idea how to approach this. If any of you can show me how to solve this, it would be most appreciated.

if the DE is

then

... most probably a typo by biff to put

Re: Solve the initial value problem:

The typo was not by biffboy. Andvaka originally wrote "(dy/dx) = (y+1(x-1))" which is NOT "(dy/dx)= (y+1)(x-1)".

Re: Solve the initial value problem:

If the original function actually is as written, then it is , which would need to be solved using an Integrating Factor...

Re: Solve the initial value problem:

Quote:

Originally Posted by

**Prove It** If the original function actually is as written, then it is

, which would need to be solved using an Integrating Factor...

Would you mind elaborating?

Thanks!

Re: Solve the initial value problem:

Re: Solve the initial value problem:

Quote:

Originally Posted by

**Prove It** I would, considering I have no idea if this is the actual problem. As the other posters have stated, it appears that you had tried to write

with a typo, thereby making an entirely different problem. The reason it looks wrong is because you would not usually write

.

Which is the correct problem?

or

?

Ah. It was a typo. The first is correct.

Re: Solve the initial value problem:

Sorry. Yes it should be (x-1)