Question

A student calculated a solution for a differential equation g'(x) with domain x > 0. The results are shown below. b g'(x) = cos(az) + x +1 sin(ax) b g(x) = (x + 1)2 There may have been some mistakes in the calculation. Indicate to the student which terms of the differential equation were integrated correctly. The terms are separated by a + or - sign. to a o a) First term is integrated incorrectly, second term is integrated correctly ob) First and second terms are integrated correctly c) First and second terms are integrated incorrectly

Answer 1

g'(x)= cay cax) + b Q+12 Sg' (x) dx = s ccos cax) + b xti ) dx g(x)= Scos Cax) dxt s by dx E let ax=u a= du da g(x)= Scoscu) I aut be da dx = 1 adu Xt1 g(x)= á scoy cu) du + s dr Eraxtl dv ax=1 dr=dx 12 i sin (u) + b / dr á sin cul + blocr) te Ć Scosa dx= sinx] (: St dx = inlag undo uzax V= x+1] a sin Cans + b ln (x+1)+c Sincan g(x) + bio (x1)c a First term integrated orectly, second term integrated inco meetly,