The equation P(x)y"+Q(x)y'+R(x)y=0 is said to be exact if it can be written in the form [P(x)y']'+[f(x)y]'=0, where f(x) is to be determined in terms of P(x), Q(x), and R(x). The latter equation can be integrated once immediately, resultingin a first order linear equation for y that can be solved. By equating the coefficients of the preceding equations and then eliminating f(x), show that a necessary condition for exactness is P"(x)-Q'(x)+R(x)=0.
I don't understand how to equate the coefficients and I was stuck after taking the integral of [P(x)y']'+[f(x)y]'=0 and got [P(x)y']+[f(x)y]=0
I don't understand how to equate the coefficients and I was stuck after taking the integral of [P(x)y']'+[f(x)y]'=0 and got [P(x)y']+[f(x)y]=0