Posted by **Mischa** on Thursday, January 24, 2008 at 4:24pm.

Find m and b so that y=mx+b is a solution to the differential equation

dy/dx=1/2x+y-1

- calc -
**drwls**, Thursday, January 24, 2008 at 4:39pm
I will assume you mean (1/2)x and not 1/(2x)in the differential equation

dy/dx = m, so we require that

m = x/2 + mx+ b -1

This is true if m = -1/2 and

b = 1+m = 1/2

y = -x/2 + 1/2 is a solution, but not the only solution, to the differential equation.

- calc -
**Damon**, Thursday, January 24, 2008 at 4:40pm
dy/dx=(1/2)x + y - 1

I assume that is what you mean.

y = m x + b

dy/dx = m

so

m = .5 x + mx + b - 1

m = (.5 + m) x + b-1

well if m is to be constant, m must be -.5

that means

-.5 = b-1

b = .5

so

y = -.5 x + .5

--------the end -----

Now check with m = -.5 and b = +.5

y = -.5 x + .5

dy/dx = -.5

dy/dx = .5 x + (-.5 x +.5) - 1

= +.5 - 1

= -.5

check

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