Question

Consider dy/dx = 1/2x + y -1
a) Find the values of the constants m and b, for which y = mx+ b is a solution to the differential equation.

Answer 1

I got the same thing but I can't find out the value of b or m?

Answer 2

There's another part of the question before this one. But I don't know if it's related to solving this one. I'll put in out just in case.
Let y = f(x) be a particular solution to the differential equation with the initial condition f(0) = 1.

Answer 3

let's plug in y(0)

m=b-1

Answer 4

Where did the x go?

Answer 5

let's plug in y(1)

m= 1/2 +(m+b) -1

1/2 + m+ b -1

two equation two unkown

Answer 6

I plug in 0 for x in first one, 1 for x in second one

Answer 7

\[m\to -\frac{1}{2},b\to \frac{1}{2}\]

Answer 8

y= -1/2 x + 1/2 should work

Answer 9

Thanks, I get it. But, if I face something on this level on my midterm, I think I'm still going to get roasted no matter how much I study.

Answer 10

what class is that from?

Answer 11

calculus

Answer 12

oh, I've taken differentials, even then It took me some time as you can see

Answer 13

There's a class called differentials? Wow. I'm just in plain calculus ab/bc. There's always some little holes I drop into when I do math.