Practise verification questions by differentiating a proposed function and checking whether it satisfies the given differential equation and conditions.
Given the following differential equation
tart fraction numerator d y over denominator d x end fraction equals x minus
2 y plus 1
(d) For which values of m and b is the line y=m x+b a solution to the
differential equation?
(d) m is the slope
ft parenthesis start fraction numerator d y over denominator d x
end fraction right parenthesis
so replace into the differential equation:
- Line 1: m equals x minus 2 left parenthesis m x plus b right parenthesis plus 1
equals left parenthesis 1 minus 2 m right parenthesis x plus left parenthesis 1
minus 2 b right parenthesis. Line 2: 1 minus 2 m equals 0 and 1 minus 2 b
equals m , so m equals 1 half and b equals 1 fourth.