Iam totally stuck regarding the following question…
i would like to understanding the reasoning rather than just knowing the right answer.
many !
let b(x) and a(x) be continuous functions in r, that are not constant functions.
let u(x) and v(x) be different solutions to the equation y'+a(x)y=b(x), and let α \inr.
which arguments are correct:
a. the general solution to the equation is y=u(x)+c(v(x)-u(x))
b. the general solution to the equation is y=u(x)+c(u(x)-v(x))
c. if y(x)=αu(x)-v(x) is a solution to the equation, then α=2
d. the function y(x)=v(x)/u(x) is a solution to y'+a(x)y=1
e. the function y(x)=u(x)+v(x) is a solution of the equation y'+a(x)y=2b(x)