Straight-line Solution of A Direction Field

[moy1989]

Hey people, I'm working on some math problems and I ran into one that asks me to determine the straight-line solution of the equation from the direction field.

The equation is y' = t - y and a graph of the field and a couple of curves is attached to this post.

Is the straight-line solution where the curve appears to be a straight line?

 

[Deleted member 4993]

Hey people, I'm working on some math problems and I ran into one that asks me to determine the straight-line solution of the equation from the direction field.

The equation is y' = t - y and a graph of the field and a couple of curves is attached to this post.

Is the straight-line solution where the curve appears to be a straight line?

I am not very sure exactly what you are asking - but...

for a straight -line

y' = constant

and

t - y = constant <<<< is an equation of a straight-line in (t,y) space.

 

[DR._Glockman]

dy/dt = t-y, y(t) = t-1+Ce^(-t); If the constant = 0, then we will have a linear equation (a straight line).

Let y(0)=-1, then y(0)=-1 = 0-1+C, C=0, hence y(t) = t-1

 

[DR._Glockman]

dy/dt = t-y, y(t) = t-1+Ce^(-t); If the constant = 0, then we will have a linear equation (a straight line).

Let y(0)=-1, then y(0)=-1 = 0-1+C, C=0, hence y(t) = t-1 is the solution, C =0.