Solve the following linear first order differential equations cosx dy/dx + y sinx = 1, y(/4)=0 Solution cosx dy/dx + y sinx = 1 dy/dx + y sinx/cosx = 1/cosx dy/dx + ytanx = secx Let P(x) = tanx I(x) = eint(tanx) I(x) = e-Ln|cosx| I(x) = secx (ysecx)\' = secx * sec x (ysecx)\' = sec2x Integrate both sides ysecx = tanx +c y = sinx + c cosx.