Mathematics II 3) Linear Equation (first order first degree) Alinear of ordinary differential Equation (ODE)can always be put in to the standared from dy dx+p(x)y = Q(x) p = (integration factor) → p = e√ p(x)dx eqation[y = · = e−√ p(x)dx * (√ p * Q(x) + C)] Example// Solve = ex – Y - Solution/ dy +Y= ex -> dx + p(x)y = Q(x) dx y=ep(x)dx * = p(x)=1&Q(x) = ex p = e√ p(x)dx = ef1dx = ex * ( p + Q (x) + c ) = e × = ( √ e * + e ³dx + c) * * 1 ex ex + ( e²x dx + c) = ex (½ e²x + c) = ½e* + exc Exercise: Solve dy - 3y = x² dx 189